Complex Numbers

A number in the form:

represents a complex number in Standard Form

In standard form a is called the real part of the complex number and bi (where b is a real number) is called the imaginary part 

If b=0, the number a+bi=a is a real number. If b does not equal 0, the number a+bi is called an imaginary number. A number of the form bi, where b does not equal 0, is called a pure imaginary number.

Equality of two complex numbers:

Operations with Complex Numbers:

Sum:

Difference:

Additive inverse:




So,

Complex Conjugates:
A pair of complex numbers of the form a+bi and a-bi that have a real number as their product

To find the quotient of a+bi and c+di where c and d are not both zero, multiply the numerator and denominator by the conjugate of the denominator to obtain

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