Problem 10 of 22num-010
For the imaginary unit , where , which of the following is equal to ?
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Solution walkthrough1:35
- Powers of go round a wheel of four: , , , . Each multiplication by is a quarter turn.
- Four quarter turns make a full turn, so divide: . Ten full turns, left over.
- So , and , which leaves .
- Take the leftover quarter turns from : , then , then . So .
- Traps: ignores the remainder, stops one step short, and turns the wrong way.