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?

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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?

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

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