Complex Numbers

From Department of Mathematics at UTSA
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A complex number is a number of the form where is the real part of the complex number, and is the imaginary part of the complex number. If , then is a real number. If and b is not equal to 0, the complex number is called an imaginary number. The imaginary unit , and can be used to express other imaginary numbers (for example, ). Note that , , , , and so on. The "complex conjugate" of is , and , which is a real number. The complex conjugate is useful for simplifying expressions involving complex numbers (for example, see complex division below).

Operations with Complex Numbers

Addition: Given two complex numbers and , . For example, .

Subtraction: .

Multiplication:

Division: Division works a bit differently with complex numbers. The reciprocal of a complex number .

So, . Note that c and d cannot both be equal to 0.

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