# How do you divide (6-6i)/(-4i)?

Aug 21, 2016

$\frac{6 - 6 i}{-} 4 i = \frac{3}{2} + \frac{3}{2} i$

#### Explanation:

In any question involving multiplication or division of complex number, one should always remember ${i}^{2} = - 1$.

In division the way is to rationalize the denominator. As we have only imaginary component in denominator, simply multiplying numerator annd denominator by $i$ should rationalize denominator.

Hence, $\frac{6 - 6 i}{- 4 i}$

= ((6-6i)×i)/(-4i×i)

= $\frac{6 i - 6 {i}^{2}}{- 4 {i}^{2}}$

= (6i+6)/(-4×-1)

= $\frac{6 i + 6}{4}$

= $\frac{6}{4} + \frac{6 i}{4}$

= $\frac{3}{2} + \frac{3}{2} i$