Simplify i^18

Problem

i18

Solution

1. Identify the cycle of the imaginary unit i The powers of i repeat every four terms: i1=i i2=−1 i3=−i and i4=1

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

18÷4=4* remainder *2

3. Rewrite the expression using the property of exponents in=i(4*k+r)=ir where r is the remainder.

i18=i(4*(4)+2)

4. Simplify the expression by substituting the known value for i2

i18=(i4)4⋅i2

i18=(1)4⋅(−1)

Final Answer

i18=−1

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