SAT Mathematics Practice Test 2

To perform the division $\frac{3-5\mathit{i}}{8+2\mathit{i}}$ multiply the numerator and denominator of $\frac{3-5\mathit{i}}{8+2\mathit{i}}$ by the conjugate of the denominator,$8-2\mathit{i}$.This gives .Since ${\mathit{i}}^2=-1$,this can be simplified to $\frac{24-6\mathit{i}-40\mathit{i}-10}{64+4}=\frac{14-46\mathit{i}}{68}$, which then simplifies to$\frac{7}{34}-\frac{23\mathit{i}}{34}$
Choices A and B are incorrect and may result from misconceptions about fraction.For example,$\frac{\mathit{a}+\mathit{b}}{\mathit{c}+\mathit{d}}$ is equal to $\frac{\mathit{a}}{\mathit{c}+\mathit{d}}+\frac{\mathit{b}}{\mathit{c}+\mathit{d}}$ not $\frac{\mathit{a}}{\mathit{c}}+\frac{\mathit{b}}{\mathit{d}}$.Choice D is incorrect and may result from a calculation error