Find the missing complex number.
-$$\frac { ? } { 6 + 6 i } = 7 - 9 i$$
A) $- 12 + 96 i$
B) $96 + 12 \mathrm { i }$
C) $96 - 12 \mathrm { i }$
D) $- 54 \mathrm { i } ^ { 2 } - 12 \mathrm { i } + 42$

Question

Quizplus · Accepted Answer

To solve the problem, we need to multiply both numerator and denominator of the left-hand side of the equation by the complex conjugate of the denominator, which is $6-6i$. This will eliminate the imaginary term in the denominator.
\begin{align*}
\frac{?}{6+6i} &= 7-9i\
\frac{?}{6+6i}\cdot\frac{6-6i}{6-6i} &= (7-9i)\cdot\frac{6-6i}{6-6i}\
\frac{? \cdot (6-6i)}{36+36} &= \frac{42-54i+42i-54i^2}{36}\
\frac{? \cdot (6-6i)}{72} &= \frac{96-54\cdot(-1)}{36}\
\frac{? \cdot (6-6i)}{72} &= \frac{240}{36}\
? &= \frac{240\cdot72}{36\cdot6} = 96-12i
\end{align*}
Therefore, the answer is $\boxed{	extbf{(C)}}$.

Find the Missing Complex Number ?6+6i=7−9i\frac { ? } { 6 + 6 i } = 7 - 9 i6+6i?​=7−9i

Find the Missing Complex Number $\frac { ? } { 6 + 6 i } = 7 - 9 i$