Use the Binomial Theorem to expand the complex number.Simplify your result. $( 5 + i ) ^ { 4 }$
A) $480 i - 476$
B) $- 480 i - 476$
C) $- 480 i + 476$
D) $480 i + 476$
E) $480 i + 476 i$

Question

Use the Binomial Theorem to expand the complex number.Simplify your result.   $( 5 + i ) ^ { 4 }$  
A) $480 i - 476$
B) $- 480 i - 476$
C) $- 480 i + 476$
D) $480 i + 476$
E) $480 i + 476 i$

Quizplus · Accepted Answer

Using the Binomial Theorem, we have:$( 5 + i ) ^ { 4 } = 5^4 + 4(5^3)(i) + 6(5^2)(i^2) + 4(5)(i^3) + (i^4)$$= 625 + 500i - 150 + 20i - 1$$= 475 + 520i$

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

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