# Complex Number Division Formula

A Complex number is in the form of a+ib, where a and b are real numbers the i is called the imaginary unit. i has the property that is $i^{2}$ = $-1$.

To find the division of any complex number use below-given formula.

Let two complex numbers are a+ib, c+id, then the division formula is,

$\LARGE \frac{a+ib}{c+id}=\frac{ac+bd}{c^{2}+d^{2}}+\frac{bc-ad}{c^{2}+d^{2}}i$

#### Solved Examples

Question 1: Divide the complex roots. $\large \frac{7 + 6i}{2 + 3i}$

Step 1 – $\large \frac{7-6i}{2-3i}\times \frac{2+3i}{2+3i}$

Step 2 – $\large \frac{14+21i-12i-18i^{2}}{4+6i-6i-9i^{2}}$

Step 3 – $\large \frac{14+21i-12i-18(-1)}{4+6i-6i-9(-1)}$

= $\large \frac{14+21i-12i+18}{4+6i-6i+9}$

Step 4 – $\large \frac{32+9i}{13}$

Step 5 – $\large \frac{32}{13}+\frac{9}{13}i$

#### Practise This Question

The food shown in the given picture is a source of a type of vitamin which helps our body to use calcium for bones and teeth. Identify the vitamin which is also produced by our body on exposure to the sunlight.