Write the complex conjugate of the following complex number and then multiply the number by the complex conjugate. Write the result in standard form.
$$1 + \sqrt { - 20 }$$
A) $1 - 20 i ; 19$
B) $1 - 5 \sqrt { 2 } i ; 21$
C) $- 1 - 2 \sqrt { 5 } i ; 21$
D) $- 1 - 2 \sqrt { 5 } i ; 19$
E) $1 - 2 \sqrt { 5 } i ; 21$

Question

Quizplus · Accepted Answer

The complex conjugate of $1 + \sqrt{-20}$ is $1 - \sqrt{-20}$ or $1 - 2\sqrt{5}i$, since $\sqrt{-20} = \sqrt{20}\sqrt{-1} = 2\sqrt{5}i$. Multiplying the number by its complex conjugate gives $1^2 - (2\sqrt{5}i)^2 = 1 - 4(5)(-1) = 1 + 20 = 21$.

Write the Complex Conjugate of the Following Complex Number and Then