Question

Simplify the following quotient of complex numbers into the form a + bi. (-8-8i)/(1+2i) is 7-6i the correct answer or am I doing this wrong?

Answer 1

Multiply top and bottom by (1+2i), so (-8-8i)(1+2i)/(1+2i)(1-2i). What does that get you?

Answer 2

So the question is this:
-8-8i/1+2i
Now, you don't want a denominator in form a+ib right?
So, just multiply both numerator and denominator with 1-2i which is the conjugate of 1+2i.
We get:
\[-8+16i-8i+16i ^{2}\] as numerator and,
\[1-4i ^{2}\] as denominator.
We know that, \[i ^{2}=-1\]
So substituting the value, we get:
-8+8i-16 as numerator and,
1+4= 5 as denominator.
Now, just put them in p/q form, you have:
8i-24 as the numerator,
and 5 as denominator.
Take 8 common from the numerator, we are left with:
8/5*(i-3)
Which is the final answer.