# How do you divide (5i)/(6+8i)?

Dec 10, 2016

The answer is $= 0.4 + 0.3 i$

#### Explanation:

${z}_{1} / {z}_{2}$

You multiply the numerator and denominator by the conjugate of the denominator

$\frac{{z}_{1} \cdot {\overline{z}}_{2}}{{z}_{2} \cdot {\overline{z}}_{2}}$

If $z = a + i b$

Then, $\overline{z} = a - i b$

and ${i}^{2} = - 1$

$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

Here,

$\frac{5 i}{6 + 8 i} = \frac{\left(5 i\right) \left(6 - 8 i\right)}{\left(6 + 8 i\right) \left(6 - 8 i\right)}$

$= \frac{30 i - 40 {i}^{2}}{36 - 64 {i}^{2}}$

$= \frac{40 + 30 i}{100}$

$= 0.4 + 0.3 i$