Simplify i^6*1

Problem

i6⋅1

Solution

1. Simplify the expression by removing the identity element, as multiplying any value by 1 does not change its value.

i6⋅1=i6

2. Identify the cycle of the imaginary unit i where i1=i i2=−1 i3=−i and i4=1

in=i(n* mod *4)

3. Divide the exponent by 4 to find the remainder.

6=4*(1)+2

4. Rewrite the expression using the remainder to find the equivalent power of i

i6=i2

5. Substitute the known value of i2

i2=−1

Final Answer

i6⋅1=−1

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