Use the Binomial Theorem to expand the complex number. Simplify your result. $( - 2 + 5 i ) ^ { 4 }$
A) $41 + 840 i$
B) $41 - 840 i$
C) $- 41 + 840 i$
D) $- 41 - 840 i$
E) 16

Question

Quizplus · Accepted Answer

Using the Binomial Theorem, we have:$$( - 2 + 5 i ) ^ { 4 } = (- 2 ) ^ { 4 } + 4 ( - 2 ) ^ { 3 } ( 5 i ) + 6 ( - 2 ) ^ { 2 } ( 5 i ) ^ { 2 } + 4 ( - 2 ) ( 5 i ) ^ { 3 } + ( 5 i ) ^ { 4 }$$$$= 16 - 40 ( 5 i ) + 60 ( - 25 ) + 40 ( 125 i ) + 625$$$$= 41 + 840 i$$

Use the Binomial Theorem to Expand the Complex Number (−2+5i)4( - 2 + 5 i ) ^ { 4 }(−2+5i)4

Use the Binomial Theorem to Expand the Complex Number $( - 2 + 5 i ) ^ { 4 }$