Perform the indicated operation. Write the answer in the form a + bi.
-$$( 8 - 5 i ) ^ { 2 } + ( 8 + 5 i ) ^ { 2 }$$
A) $64 - 160 i$
B) $78 + 160 i$
C) 64
D) 78

Question

Quizplus · Accepted Answer

Expanding both terms: $(8 - 5i)^2 = 64 - 80i + 25i^2$ and $(8 + 5i)^2 = 64 + 80i + 25i^2$. Since $i^2 = -1$, both expansions simplify to $64 - 80i - 25$ and $64 + 80i - 25$ respectively. Adding them together: $64 - 25 + 64 - 25 = 128 - 50 = 78$, with the imaginary parts canceling out.

Perform the Indicated Operation (8−5i)2+(8+5i)2( 8 - 5 i ) ^ { 2 } + ( 8 + 5 i ) ^ { 2 }(8−5i)2+(8+5i)2

Perform the Indicated Operation $( 8 - 5 i ) ^ { 2 } + ( 8 + 5 i ) ^ { 2 }$