Indicate whether the statement is true always, sometimes, or never.
-$$\text { To find the quotient } \frac { 5 + 8 \mathrm { i } } { 5 - 8 \mathrm { i } } \text {, multiply numerator and denominator by } 5 + 8 \mathrm { i } \text {. }$$
A) Never
B) Sometimes
C) Always

Question

Quizplus · Accepted Answer

To find the quotient of complex numbers in the form $\frac{a+bi}{c+di}$, one common method is to multiply both the numerator and denominator by the conjugate of the denominator to eliminate the imaginary part in the denominator. In this case, the conjugate of $5 - 8i$ is $5 + 8i$, so multiplying both the numerator and denominator by $5 + 8i$ is the correct method to simplify the expression. This approach is always used to simplify complex number divisions.

Indicate Whether the Statement Is True Always, Sometimes, or Never