Perform the indicated operation and simplify. Write the result in the form a + bi.
-$$( 4 + 10 \mathrm { i } ) ^ { 2 }$$
A) $16 + 100 \mathrm { i }$
B) $- 84 + 80 \mathrm { i }$
C) $116 + 80 \mathrm { i }$
D) $16 - 100 \mathrm { i }$

Question

Quizplus · Accepted Answer

To simplify $(4 + 10i)^2$, we first expand it using the formula $(a + bi)^2 = a^2 + 2abi + b^2i^2$. Here, $a = 4$ and $b = 10$, so we get $4^2 + 2 \cdot 4 \cdot 10i + (10i)^2 = 16 + 80i - 100$, because $i^2 = -1$. Simplifying, we get $-84 + 80i$.

Perform the Indicated Operation and Simplify (4+10i)2( 4 + 10 \mathrm { i } ) ^ { 2 }(4+10i)2

Perform the Indicated Operation and Simplify $( 4 + 10 \mathrm { i } ) ^ { 2 }$