What is Artificial Intelligence?


Artificial intelligence is the capacity for adapting and learning. It can be found in video games, personal assistants and even self-driving cars.

AI systems can be divided into weak and strong types. Weak AIs tend to be reactive, optimizing outputs based on inputs; on the other hand, strong AIs possess limited memory and are programmed to solve problems without human assistance.

Imaginary number

The imaginary number i is a non-zero real number with the property of being squared to produce a negative value. This property of square roots of negative numbers makes it essential for understanding complex mathematic equations, as well as being part of complex numbers themselves.

Imaginary numbers are a valuable addition to the set of real numbers, as they enable mathematicians to describe various complex structures and operations. In particular, they can be employed in modeling mathematical functions which would otherwise be difficult to calculate.

Before the discovery of imaginary numbers, mathematicians struggled to solve equations that couldn’t be solved with only real numbers. However, once it was discovered that an imaginary number could be used for these problems, they could apply them in many different fields such as electrical engineering and quantum physics.

Girolamo Cardano, an Italian mathematician in the 16th century, was the first to explore imaginary numbers. At first sceptical, he labeled his methods as “sophistry,” but eventually came around to understanding their potential use in mathematics.

He even devised a formula for calculating the square root of an imaginary number that is still used today: “In ir, where r is the remainder after dividing n by 4 if n is not zero.”

Another useful rule is to multiply an imaginary number with its conjugate pair of denominators. The imaginary number will multiply itself leftward while its conjugate pair moves rightward, providing a solution with identical coefficients as when multiplying real numbers by conjugate pairs of denominators.

Therefore, imaginary numbers are invaluable in advanced calculus and various mathematical proofs. They appear in equations that don’t touch the x axis, making them especially useful for representing waves.

Physics researchers have shown that when quantum physics fails to account for imaginary numbers, the world becomes inaccurately described. In December and January experiments at USTC, two separate teams demonstrated this truth when playing an experiment called the Bell game inside a quantum computer. Furthermore, researchers at University of California Santa Barbara reconstructed an atom’s wave function which cannot be fully described with real numbers alone.

Argand plane

The Argand plane is a two-dimensional representation of complex numbers. It resembles the Cartesian plane, except instead of having x and y axes it uses real and imaginary ones.

The Argand plane was created by Jean-Robert Argand (1768-1822), an amateur mathematician living in Paris. In his self-published essay, he demonstrated how to represent imaginary quantities using geometric constructions; this method made complex numbers much more approachable to mathematicians.

One of the key applications of the Argand plane is control theory, where it can be utilized to graphically represent equation roots and determine stability in closed-loop systems.

It can also be utilized for calculating the frequency at which a system can withstand an overload. The Argand plane can be graphed to observe how magnitude and phase responses alter over time.

Similarly, the complex plane can be employed to plot the zeros and poles of a function. It is an invaluable tool in analyzing electron loss spectra.

A polar representation of a complex number in the argand plane is known as the modulus-argument form. The modulus is the length of the hypotenuse, while the argument is an angle made between it and the real axis.

This method of representing complex numbers on a two-dimensional plane simplifies complex calculations. It’s similar to the method for locating a point on the Cartesian plane, where the real axis is the x-axis and the imaginary axis is the y-axis.

To locate a complex number in an Arand plane, draw a straight line connecting the x-axis to an imaginary axis and then from the y-axis to the real axis. This is similar to how one would locate a point on a sphere’s surface with its one-to-one connection with its north pole.

Caspar Wessel invented the Argand plane, but it is more commonly associated with Jean-Robert Argand. His initial diagram of this type was published in Annales de mathematiques pures et appliees (Annales of Mathematics Pure and Applied), 1806.


Exponents are mathematical symbols or numbers that represent how many times something has been multiplied. They’re also referred to as powers or indices and play an essential role in algebra and calculus, though their use can be confusing for those new to mathematics.

Raising a number to an exponent makes it simpler to write its product. For instance, 35 is written as 3*3*3+5; this is because three appears five times in multiplication.

Another thing you may have observed is the repeating pattern of i to the fourth power and i to the 96th power in this table. This sequence repeats every four powers.

i to the 500th power is similar, following a pattern similar to i to the fourth power’s pattern of 125th powers. This cycle repeats until you reach either 1000th power (i-1) or first power (1-1).

One of the key properties of exponents is that when a quantity in parentheses is raised to a power, it only applies to that portion within parentheses. Subsequently, when that same quantity is raised to another power, it will apply to everything inside again.

Luisa and Michele have successfully simplified the original expression using exponentiation properties, providing a great opportunity to learn about this important area of math!

In addition to multiplying powers, exponents can be used to simplify complex expressions. This is especially helpful when working with alternating sequences as it makes them much clearer and simpler to comprehend. Furthermore, understanding these laws of exponents will prove beneficial in algebra; hence its importance should not be overlooked.

Multiplication and division

Multiplication and division are the foundational math concepts that children in elementary school must master to progress to more complex math lessons. Without these fundamental abilities, students will not be able to comprehend more intricate mathematical ideas.

When learning multiplication, it is essential for students to recognize the commutative property. This principle states that the order of numbers in a multiplication equation does not affect its outcome. Mastering this skill will enable learners to memorize facts more quickly and free up time for other skills in the curriculum.

One way to help students retain their multiplication facts is through skip counting. This strategy involves adding a number each time they skip over the previous one and can be applied for many different types of problems.

Students can practice multiplying and dividing using arrays. Arrays provide an engaging way to demonstrate spatial relationships, helping students connect multiplication and division concepts to measurement.

In addition, arrays are an invaluable teaching aid when teaching the concept of area. This concept may be difficult for younger students to comprehend, so using an array to demonstrate its relationship to multiplication and division is a great place to start.

Exposing students to new applications of division, such as fraction division, can be beneficial. The connection between multiplication and division is strong, which helps students better comprehend fractions when interpreting them.

Multiplication and division have a powerful effect, so it is essential that your students become acquainted with as many types of division as possible. Doing this will give them insight into various strategies and enable them to choose which works best for them.

For instance, they might wish to learn how to divide a whole number by an unknown factor in a word problem. To do this, they must be able to determine the appropriate factor by solving for its quotient.

Students should also be taught the commutative property of division. This property states that the order of divisor and quotient does not affect the final result. This knowledge is essential for successfully completing grade level math worksheets and other division tasks.


What Is Artificial Intelligence?

You might have been familiar with the term “artificial intelligence” or AI, as it has gained wide popularity. Even today’s gadgets are powered by AI even though for limited and specific uses. Actually, artificial intelligence refers to a more complex and wider discipline than today’s limited implementation. Let’s learn how artificial intelligence works.

What Is Artificial Intelligence?

Artificial Intelligence is generally defined as complex software that works similar to human brains and can perform its tasks. In the computing context, artificial intelligence is designed to mimic the brain ware(human). AI basically sense and respond to elements or dynamics in a contextual environment. At this point, AI has similar abilities to human brains, including solving problems in creative and intuitive ways. While AI was programmable, it’s developed in certain ways to emphasize its independence and autonomous features.

At this point, a question might have arisen about what and how artificial intelligence can differ from other computer programs we already know. Generally speaking, AI is a more complex software designed to comprehend and solve diverse problems beyond contextual manners. On the other hand, conventional programs are designed to solve particular computing tasks with no intuition. AI development and implementations are projected to help us solve the most complex, biggest, and most urgent issues with a focus on solutions.

How It Works

Basically, AI works by simulating the process of human intelligence with what’s called machine learning. This machine learning is employed with a program containing and implementing sets of recorded information that’s already known to new contexts or experience. This machine would then technically learn how to process the recorded information while elaborating it with new environment/cases/features of experience it’s currently sensing before responding. In other words, this elaboration and decision-making result from the machine’s learning process that powers AI.

Machine learning has gone through advancements these years. The main advantage of machine learning is that it can comprehend big amounts of data and find patterns accurately that humans can’t perform. In other words, advanced machine learning is outsmarting what it’s mimicking, the human brain, to some extent.

What’s more fundamental that machine learning provides to AI implementation is its ability to make decisions. Machine learning can learn deeper and more than patterns as they would soon make decisions independently. Even now, AI can suggest solutions, whether it’s to filter your photo in real-time or to analyze your game playing performance. At this point, machine learning has already driven challenges to humanity as soon as they can make decisions on their own. The ability of machine learning could be unexpected.

Challenges and Alerts

AI adoptions drive many challenges for humanity and alerts from scientists and tech experts. They’ve been warning about the risks of the broadened, massive AI implementation. Like in Hollywood Sci-Fi movies, AI’s uncontrolled adoption would lead them to outsmart humans and become more extremely intelligent, where human brains can’t even catch up with the process. It’s because they’re basically learning from new experiences, even for now. If that’s what happens, human intelligence is no longer needed. 

Even today’s AI developments have sounded those predicted-alerts. Some computer labs and scientists currently focusing on AI development have to keep projects from the public as they’re too intelligent and could be very dangerous. Today, AI adoptions have changed how we communicate, socialize, work, act, and even behave. AI would undoubtedly shape the future but how it should be adopted remains challenging.

Today’s AI Adoptions

AI technology has been already adopted in various areas, including

Banking and Finance

AI adoption in banking and finance has been growing progressively. Banks use AI to analyze transactions’ behaviors and natures so they can identify and prevent fraudulent activities. Finance and investment companies adopt AI to improve their platform’s performance, analyze market conditions, and provide better services to their clients.


Agricultural sectors have also adopted AI, especially to overcome general issues and to improve food productions. AI contributes to improving the sustainability and efficiency of the agriculture system in several ways. AI offers innovative approaches to overcome general farming issues, including weather, crop protection, fertilizing, deficiencies, potential defects, and so forth. AI can help our farmers to find insightful information about efficient farming and solutions to their problems. AI would contribute to food security from now on.

Digital Marketing

AI has been employed by corporations for years to support their digital marketing campaign. The artificial intelligence manifested in the applied algorithm helps companies learn audience behavior and helps them build the best possible strategies to market their products and services. Whether it’s an e-commerce marketplace or an individual business site, marketing business gets easier with AI helps.


Healthcare industries are getting relied on AI in handling complicated tasks. Hospitals use a clinical decision support system that warns doctors or physicians about their patients’ particular health risks. Some healthcare devices are employed to diagnose particular health conditions that need specific treatments. More hospitals also employ AI-powered systems to keep track of at-home patients.

Autonomous Vehicles

Automotive industries are the obvious clients of AI following their ambitious mission in autonomous vehicles. The autonomous vehicle idea isn’t only revolutionary, but more auto companies have also progressively developed and produced ones. AI allows the system to collect real-time data from GPS, sensors, cameras, storage and presets to autonomously operate the car. Even public transport is converting into a fully autonomous system.

Social Media

It’s no longer a secret that social media platforms are using AI throughout their services. These include face-detecting verifications, news feed design & content, personalized services, filtering inappropriate content, and many more. For example, AI and machine learning have helped the admins of social media platforms block or ban offensive and inappropriate content, whether they’re texts, photos, videos, or sounds.

There are actually more AI adoptions you can experience even for now, including customer service chatbots, gaming, artificial creativity, and so forth. In the future, AI would be adopted in most aspects of our lives.

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