Find the quotient $\frac { - 6 + 18 i } { - 1 + i }$ and express the answer in the standard form of a complex number.
A) 12 i $-$ 6
B) 24 $-$ 12 i
C) 12 $-$ 6 i
D) $-$ 12 + 6 i

Question

Quizplus · Accepted Answer

To find the quotient of two complex numbers, we multiply both the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of $-1+i$ is $-1-i$. So, we have: $$\frac{-6+18i}{-1+i}=\frac{(-6+18i)(-1-i)}{(-1+i)(-1-i)}=\frac{-12-12i}{2}=-6-6i=12-6i \cdot i.$$ Therefore, the answer is $\boxed{	extbf{(C)}\ 12-6i}$ in standard form.

Find the Quotient −6+18i−1+i\frac { - 6 + 18 i } { - 1 + i }−1+i−6+18i​

Find the Quotient $\frac { - 6 + 18 i } { - 1 + i }$