Perform the indicated operation. Write the result in the form a + bi.
-$$( 2 + 8 i ) ^ { 2 }$$
A) $4 + 32 i + 64 i ^ { 2 }$
B) $68 + 32 i$
C) $- 60 + 32 i$
D) $- 60$

Question

Quizplus · Accepted Answer

To solve $(2 + 8i)^2$, we first apply the formula $(a + bi)^2 = a^2 + 2abi + b^2i^2$. Here, $a = 2$ and $b = 8$, so we get $2^2 + 2*2*8i + (8i)^2 = 4 + 32i + 64i^2$. Since $i^2 = -1$, we replace $64i^2$ with $64(-1)$, resulting in $4 + 32i - 64$, which simplifies to $-60 + 32i$.

Perform the Indicated Operation (2+8i)2( 2 + 8 i ) ^ { 2 }(2+8i)2

Perform the Indicated Operation $( 2 + 8 i ) ^ { 2 }$