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

• $5-4i$