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N-CN.1 Warmup M2-055-A01-V04

Understand i as a number with i^2=-1 and represent complex numbers as a+bi.

Simplify powers of $i$ using the repeating cycle $i, -1, -i, 1$

Problem

Evaluate \(i^{32}\) by dividing \(32\) by \(4\), using the remainder to locate the power in the cycle \(1,i,-1,-i\), and stating the result.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
N-CN.1
Category
Number and Quantity
Domain
The Complex Number System
Objective
Understand i as a number with i^2=-1 and represent complex numbers as a+bi.
Problem type
Simplify powers of $i$ using the repeating cycle $i, -1, -i, 1$