PrerequisitesPrerequisite

Powers of

Use the four-step cycle of powers of the imaginary unit.

  • , so the cycle is .
  • Divide a positive exponent by 4 and use its remainder to locate the cycle position.

Example 1

Reduce the exponent

Simplify the expression.

Example 2

A multiple of four

Fully simplify the expression.

Your turn

Question 1

Simplify.

Check answer
Question 2

Simplify.

Check answer
Question 3

Simplify.

Check answer
Question 4

Simplify.

Check answer
Question 5

Simplify.

Check answer
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