SAT Mathematics Practice Test 4

To rewrite $\frac{8-\mathit{i}}{3-2\mathit{i}}$ in the standard form a + bi, multiply the numerator and denominator of $\frac{8-\mathit{i}}{3-2\mathit{i}}$ by the conjugate, $3+2\mathit{i}$.This gives .Since ${\mathit{i}}^2=-1,$ this last fraction can be rewritten as $\frac{24+16\mathit{i}-3\mathit{i}+2}{9-\left(-4\right)}=\frac{26+13\mathit{i}}{13}$ which simplifies to 2 + i.Therefore, when $\frac{8-\mathit{i}}{3-2\mathit{i}}$ is rewritten in the standard form $\mathit{a}+\mathit{b}\mathit{i},$ the value of a is 2.
Choices B, C, and D are incorrect and may be the result of errors in symbolic manipulation. For example, choice B could be the result of mistakenly rewriting $8-\mathit{i}3-2\mathit{i}$ as$\frac{8}{2}+\frac{1}{2}\mathit{i}$