How do you simplify #(4+4i)/(2i)#?

1 Answer
Sep 29, 2016

Answer:

Multiply by the complex conjugate in both the numerator and denominator.

Explanation:

To simplify this expression, we need to remove the imaginary component in the denominator.

So, we multiply by the complex conjugate of #2i# which is #-2i# on both the numerator and denominator

#(4+4i)/(2i) * ((-2i)/(-2i))#

# ((-2i)/(-2i))# evaluates to 1, so multiplying by it does not change the value of our expression.

Multiplying through, we find #(-8i-8i^2)/(-4i^2)#

We know #i^2 = -1#, so we replace in the expression and get:

#(-8i+8)/4#

Since all terms have a 4, we can divide through by it, getting our answer:

#-2i+2#