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

1 Answer
Jul 21, 2016

Answer:

#-1+i#

Explanation:

We can multiply the top and bottom of a fraction by the same thing without changing the value of the fraction. Combining this with the fact that the product of a complex number with it's complex conjugate will be real gives us a handy trick for dividing by complex numbers - multiply numerator and denominator by the conjugate!

#(-4-4i)/(4i)*(-4i)/(-4i)#

#=(16i + 16i^2)/(-16i^2)#

Recall that #i^2 = -1#

#=(16i - 16)/(16) = -1 + i#