Find the missing complex number.
-$$\frac { ? } { 7 + 9 i } = 8 + 9 i$$
A) $137 + 9 i$
B) $- 25 + 135 i$
C) $- 25 - 135 \mathrm { i }$
D) $81 i ^ { 2 } + 135 i + 56$

Question

Quizplus · Accepted Answer

We can approach this problem by multiplying both sides by the denominator $7+9i$:
$$\frac{?}{7+9i}(7+9i)=(8+9i)(7+9i)$$
Simplifying the right side using FOIL (First, Outer, Inner, Last) method, we have:
$$(56+8\times9i+63i+81i^2)=(56+135i-81)$$
Simplifying further and noticing that $i^2=-1$, we get:
$$25+144i=-56+135i$$
Finally, solving for the missing complex number, we get:
$$\frac{?}{7+9i}=8+9i\Rightarrow ?=(8+9i)(7+9i)=\boxed{-25+135i}$$

Find the Missing Complex Number ?7+9i=8+9i\frac { ? } { 7 + 9 i } = 8 + 9 i7+9i?​=8+9i

Find the Missing Complex Number $\frac { ? } { 7 + 9 i } = 8 + 9 i$