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