# How do you write the complex conjugate of the complex number 1 + 3i?

Nov 9, 2016

The conjugate is $= 1 - 3 i$

#### Explanation:

Let $z = a + i b$ be a complex number

The conjugate is $\overline{z} = a - i b$

Therefore, $z \cdot \overline{z} = \left(a + i b\right) \left(a - i b\right)$

$= {a}^{2} - {i}^{2} {b}^{2}$
But ${i}^{2} = - 1$

therefore $z \cdot \overline{z} = {a}^{2} + {b}^{2}$