Simplify by rationalizing the denominator. Write your answer in a +bi form.
-$\frac { 2 + 3 i } { 5 + 2 i }$
A) $\frac { 4 } { 29 } - \frac { 19 } { 29 } \mathrm { i }$
B) $\frac { 16 } { 29 } + \frac { 11 } { 29 } \mathrm { i }$
C) $\frac { 4 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$
D) $\frac { 16 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { 2 + 3 i } { 5 + 2 i }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $5 - 2i$. This gives $\frac{(2 + 3i)(5 - 2i)}{(5 + 2i)(5 - 2i)}$. Simplifying, we get $\frac{10 - 4i + 15i - 6i^2}{25 - 4i^2}$, which simplifies further to $\frac{16 + 11i}{29}$, or $\frac{16}{29} + \frac{11}{29}i$.

Simplify by Rationalizing the Denominator 2+3i5+2i\frac { 2 + 3 i } { 5 + 2 i }5+2i2+3i​

Simplify by Rationalizing the Denominator $\frac { 2 + 3 i } { 5 + 2 i }$