Simplify $( 5 + 2 i ) ^ { 2 } - ( 5 - 2 i ) ^ { 2 }$ and write the answer in standard form.
A) $0$
B) $40 i$
C) $50 + 40 i$
D) $50 + 8 i$
E) $10 + 8 i$

Question

Quizplus · Accepted Answer

Expanding both squares and subtracting, we get: $(5 + 2i)^2 - (5 - 2i)^2 = (25 + 20i + 4i^2) - (25 - 20i + 4i^2)$. Since $i^2 = -1$, this simplifies to $25 + 20i - 4 - (25 - 20i - 4) = 20i + 20i = 40i$.

Simplify (5+2i)2−(5−2i)2( 5 + 2 i ) ^ { 2 } - ( 5 - 2 i ) ^ { 2 }(5+2i)2−(5−2i)2

Simplify $( 5 + 2 i ) ^ { 2 } - ( 5 - 2 i ) ^ { 2 }$