Complex number

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A complex number is a number. It only sounds complex, but really is not. With algebra, you can do addition, subtraction, multiplication, and division. Using negative numbers, it is possible to find the x in the equation a + x = b for all possible values of a and b.

With multiplication and division, there is a problem. There is no (normal) number, that gives you -1, when you multiply it by itself. In other words, -1 (or any other negative number) has no square root. To solve this problem, mathematicians introduced an imaginary number called i. That imaginary number will give -1 when you multiply it by itself.

A complex number can now be written as a + bi, where a is called the real part of the number, and b is called the imaginary part. Usually, the complex number is written as (a,b). Both a and b are real numbers.

A real number can simply be written as a + 0 \cdot i or (a,0).

With complex numbers it is possible to do all the four basic calculations as defined in algebra, but also more complicated calculations.

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