Q: Why to study complex numbers?

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Yes. But until you study complex numbers, there is no solution.

Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.

No. Complex numbers is the highest set of numbers you can go, and there are no sets outside of complex numbers.

1. A complex formula like (z+1/z) is used to study and design airplane wings. 2. I use complex numbers to make math related art. The LINK below shows artwork based on the formula (z-1)/(z+i)

In the complex plane, each complex number is represented by a point, with the real part as the x-coordinate and the imaginary part as the y-coordinate. The mapping of complex numbers in the complex plane allows us to visualize operations like addition, subtraction, multiplication, and division geometrically. It also enables us to study properties such as modulus, argument, and conjugate of complex numbers.

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Yes. But until you study complex numbers, there is no solution.

Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.

Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.

No. Complex numbers is the highest set of numbers you can go, and there are no sets outside of complex numbers.

1. A complex formula like (z+1/z) is used to study and design airplane wings. 2. I use complex numbers to make math related art. The LINK below shows artwork based on the formula (z-1)/(z+i)

In the complex plane, each complex number is represented by a point, with the real part as the x-coordinate and the imaginary part as the y-coordinate. The mapping of complex numbers in the complex plane allows us to visualize operations like addition, subtraction, multiplication, and division geometrically. It also enables us to study properties such as modulus, argument, and conjugate of complex numbers.

The square of a "normal" number is not negative. Consequently, within real numbers, the square root of a negative number cannot exist. However, they do exist within complex numbers (which include real numbers)and, if you do study the theory of complex numbers you wil find that all the familiar properties are true.

Real numbers are a proper subset of Complex numbers.

In all likelihood, all the numbers that you will come across during school will belong to the Real number system.In the UK , it is only when you study "Further Pure" mathematics at A-levels, or at university that you will study complex numbers which belong to a set that is the next step beyond Real numbers.

Complex numbers were not invented by Mr KBH.

Complex numbers include real numbers, pure imaginary numbers, and the combination of those two.

Yes, the complex numbers, as well as the real numbers which are a subset of the complex numbers, form groups under addition.