Simplify i^44

Problem

i44

Solution

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

2. Recognize that the powers of i repeat in a cycle of 4.

3. Divide the exponent 44 by the cycle length 4 to find the remainder.

44÷4=11* remainder *0

4. Apply the rule that in=ir where r is the remainder of n/4

i44=i0

5. Simplify the expression using the fact that any non-zero number raised to the power of 0 is 1.

i0=1

Final Answer

i44=1

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