Question

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

Answer 1

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

Explanation:

The complex conjugate of a complex number `a+bi`, denoted `bar(a+bi)`, is given by `bar(a+bi) = a-bi`. A useful property is that the product of any number and its conjugate is a real number, that is,

`a+bi*(bar(a+bi)) in RR`

We will use that property to remove the complex part from the denominator by multiplying the numerator and denominator by the conjugate of the denominator.

`6/(-4i) = (6*(bar(-4i)))/(-4i*(bar(-4i)))`

`=(6*(4i))/(-4i*(4i))`

`=(24i)/(16)`

`=3/2i`