# How do you simplify #(-4sqrt2+4sqrt2i)div(6+6i)#?

##### 1 Answer

Nov 8, 2017

#### Explanation:

Normally when rationalising the quotient of two complex numbers you would multiply numerator and denominator by the compelx conjugate of the denominator.

In this example, the denominator is:

#6+6i = 6(1+i)#

So instead of multiplying by the complex conjugate

#(-4sqrt(2)+4sqrt(2)i)/(6+6i) = (-4sqrt(2)(1-i)(1-i))/(6(1+i)(1-i))#

#color(white)((-4sqrt(2)+4sqrt(2)i)/(6+6i)) = (-4sqrt(2)(1-2i+i^2))/(6(1-i^2))#

#color(white)((-4sqrt(2)+4sqrt(2)i)/(6+6i)) = (8sqrt(2)i)/12#

#color(white)((-4sqrt(2)+4sqrt(2)i)/(6+6i)) = 2/3sqrt(2)i#