Use the Binominal Theorem to expand the complex number.Simplify your result. $( 3 - 2 i ) ^ { 4 }$
A) $- 135 + 344 i$
B) $- 151 + 344 i$
C) $- 135 - 88 i$
D) $- 151 - 88 i$
E) $313 - 88 i$

Question

​Use the Binominal Theorem to expand the complex number.Simplify your result.​ $( 3 - 2 i ) ^ { 4 }$ ​
A)​ $- 135 + 344 i$
B)​ $- 151 + 344 i$
C)​ $- 135 - 88 i$
D)​ $- 151 - 88 i$
E)​ $313 - 88 i$

Quizplus · Accepted Answer

Using the Binomial Theorem, we get:
(2-3i)^5 = C(5,0)(2)^5(-3i)^0 + C(5,1)(2)^4(-3i)^1 + C(5,2)(2)^3(-3i)^2 + C(5,3)(2)^2(-3i)^3 + C(5,4)(2)^1(-3i)^4 + C(5,5)(2)^0(-3i)^5
Simplifying, we get:
(2-3i)^5 = 32 - 240i + 720 + 1080i -405 - 243i
(2-3i)^5 = -53 - 403i, which is equivalent to choice D.

​Use the Binominal Theorem to Expand the Complex Number (3−2i)4( 3 - 2 i ) ^ { 4 }(3−2i)4

Use the Binominal Theorem to Expand the Complex Number $( 3 - 2 i ) ^ { 4 }$