Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $- 13 + \sqrt { 12 } i$
A) $13 + \sqrt { 12 } i , 181$
B) $- 13 + \sqrt { 12 } i , 181$
C) $- 12 - \sqrt { 13 } i , 181$
D) $- 13 - \sqrt { 12 } i , 181$
E) $13 - \sqrt { 12 } i , 181$

Question

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $- 13 + \sqrt { 12 } i$ 
A) $13 + \sqrt { 12 } i , 181$
B) $- 13 + \sqrt { 12 } i , 181$
C) $- 12 - \sqrt { 13 } i , 181$
D) $- 13 - \sqrt { 12 } i , 181$
E) $13 - \sqrt { 12 } i , 181$

Quizplus · Accepted Answer

The complex conjugate of $ - 13 + \sqrt {12} i$ is $ -13 - \sqrt{12} i$.

Multiplying the original number by its complex conjugate, we get 
\begin{align*}
(-13+\sqrt{12}i)(-13-\sqrt{12}i) &= 169 -12i^2 \
&= 169 + 12 \
&= 181.
\end{align*}

Therefore, the answer is D.

Write the Complex Conjugate of the Complex Number −13+12i- 13 + \sqrt { 12 } i−13+12​i

Write the Complex Conjugate of the Complex Number $- 13 + \sqrt { 12 } i$