Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form.
$2 + \sqrt { - 27 }$
A) $2 - 27 i ; 25$
B) $2 - 3 \sqrt { 3 } i ; \quad 31$
C) $- 2 - 3 \sqrt { 3 } i ; 31$
D) $- 2 - 3 \sqrt { 3 } i ; \quad 25$
E) $\quad 2 - 3 \sqrt { 3 } i ; \quad 31$

Question

Quizplus · Accepted Answer

The complex conjugate of $2 + \sqrt { - 27 }$ is $2 - \sqrt { - 27 }$. Multiplying the number by its complex conjugate gives:$$(2 + \sqrt { - 27 })(2 - \sqrt { - 27 }) = 2^2 - (\sqrt { - 27 })^2 = 4 - (-27) = 31$$Therefore, the result is $31$ in standard form.

Write the Complex Conjugate of the Following Complex Number and Then