Evaluate the expression and write in the form $a + b i$ . $i ^ { 55 }$
A) $- i$
B) $- 55 i$
C) $- \sqrt { i }$
D) $i$
E) $- 1$

Name: Evaluate the expression and write in the form $a + b i$ . $i ^ { 55 }$ A) $- i$ B) $- 55 i$ C) $- \sqrt { i }$ D) $i$ E) $- 1$
Brand: Quizplus
Rating: 4.9 (40 reviews)

Question

Quizplus · Accepted Answer

The powers of $i$ cycle every 4 steps: $i^1 = i$, $i^2 = -1$, $i^3 = -i$, $i^4 = 1$, and then it repeats. $i^{55} = i^{(4*13 + 3)} = i^3 = -i$, because 55 divided by 4 leaves a remainder of 3.

Evaluate the Expression and Write in the Form a+bia + b ia+bi

Evaluate the Expression and Write in the Form $a + b i$