Complex conjugate

A complex conjugate pair is a pair of two complex numbers which are identical, except for that the sign of the imaginary part is different.

If w=x+yi, then the conjugate of w is x-yi.

Representing the complex conjugate

The complex conjugate of a complex number, z, is represented by z^*.

Examples of complex conjugates

5+2i and 5-2i
-i+1 and 1+i
4i and -4i

Complex roots

Complex roots come in conjugate pairs. This means that, if a complex number is a root of an equation, then the conjugate of that complex number is also a root.

Given that 5+4i is a root of an equation, find another root

5-4i

flashcards

Question	Answer
What is a complex conjugate pair?	A pair of two complex numbers identical except for the sign of their imaginary parts.
If w = x + yi, how do you find its conjugate?	The conjugate of w is x - yi.
How is the complex conjugate of z represented?	It is represented by z^*.
Give an example of a complex conjugate pair.	5+2i and 5-2i (or -i+1 and 1+i, or 4i and -4i).
What is a key property of complex roots in an equation?	Complex roots come in conjugate pairs: if a complex number is a root, its conjugate is also a root.
If 5+4i is a root of an equation, what is another root?	5-4i