# How do you write the complex conjugate of the complex number 5i?

Aug 25, 2016

$- 5 i$

#### Explanation:

For a complex number $z = \left(a + b i\right) \left\{a , b\right\} \in \mathbb{R}$, the complex number $z ' = \left(a - b i\right)$ is said to be its "complex conjugate".

[Note that the product of a conjugate pair is:
$z \times z ' = {a}^{2} + {b}^{2}$ which is real]

In this example $z = \left(0 + 5 i\right)$
So, $a = 0$ and $b = 5$ in this case

$\therefore z ' = \left(0 - 5 i\right)$ which can be written as simply $- 5 i$