Evaluate the expression $\frac { 41 } { 4 - 5 i }$ and write the result in the form a + bi.
A) $4 + 5 i$
B) $4 - 5 i$
C) $- 5 - 4 i$
D) $5 + 4 i$
E) none of these

Question

Evaluate the expression $\frac { 41 } { 4 - 5 i }$ and write the result in the form a + bi. 
A) $4 + 5 i$
B) $4 - 5 i$
C) $- 5 - 4 i$
D) $5 + 4 i$
E) none of these

Quizplus · Accepted Answer

To evaluate the expression, we can multiply both the numerator and denominator by the complex conjugate of the denominator, which is $4 + 5 i$. This gives us:$$\frac { 41 } { 4 - 5 i } = \frac { 41 } { 4 - 5 i } \cdot \frac { 4 + 5 i } { 4 + 5 i } = \frac { 41 ( 4 + 5 i ) } { 4^2 - ( 5 i )^2 }$$$$= \frac { 41 ( 4 + 5 i ) } { 16 - 25 i^2 } = \frac { 41 ( 4 + 5 i ) } { 16 + 25 } = \frac { 41 ( 4 + 5 i ) } { 41 } = 4 + 5 i$$Therefore, the answer is $4 + 5 i$, which is choice A.

Evaluate the Expression 414−5i\frac { 41 } { 4 - 5 i }4−5i41​

Evaluate the Expression $\frac { 41 } { 4 - 5 i }$