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:$$( - 2 + 5 i ) ^ { 4 } = (-2)^4 + 4(-2)^3(5i) + 6(-2)^2(5i)^2 + 4(-2)(5i)^3 + (5i)^4$$$$= 16 - 80i + 60 - 200i + 625$$$$= 41 - 840 i$$

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 $( - 2 + 5 i ) ^ { 4 }$