Solve. Give exact solutions.
-$$( x - 1 ) ^ { 2 } = - 16$$
A) $1 \pm 4 \mathrm { i }$
B) $1 \pm 4$
C) $4 \mathrm { i }$
D) $4 \mathrm { i } + 1$

Question

Quizplus · Accepted Answer

We first need to isolate x, so we take the square root of both sides:
\begin{aligned} \sqrt{(x-1)^2} &= \sqrt{-16} \ |x-1| &= 4i \end{aligned}
Now we have two cases to consider: 
Case 1: x-1 = 4i 
Adding 1 to both sides gives x = 1 + 4i. 
Case 2: x-1 = -4i 
Adding 1 to both sides gives x = 1 - 4i. 
Therefore the solutions are x = 1+4i or x = 1-4i, which can also be written as x=1±4i. Therefore, the best choice is A.

Solve Give Exact Solutions (x−1)2=−16( x - 1 ) ^ { 2 } = - 16(x−1)2=−16

Solve Give Exact Solutions $( x - 1 ) ^ { 2 } = - 16$