Question

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

Answer 1

`(6-6i)/-4i=3/2+3/2i`

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, `(6-6i)/(-4i)`

= `((6-6i)×i)/(-4i×i)`

= `(6i-6i^2)/(-4i^2)`

= `(6i+6)/(-4×-1)`

= `(6i+6)/4`

= `6/4+(6i)/4`

= `3/2+3/2i`