Evaluate these powers of i

Question

Evaluate these powers of i.If there is an imaginary part,be sure to enter your answer in a+bi form,where both a and b are real numbers

 

i¹¹¹³

 

i^-147

Answer 1

Since the powers 0 through 3 of i yield results 1, i, - 1 and -i, respectively, and this cycle repeat for the powers 4 through 7, etc, all you have to do is divide the exponent by 4 and just use the Remainder, e.g.

i¹⁰¹= i¹⁰⁰•i ⁼ i. 

 

So i¹¹¹³ = i.  I'll let you do the second example yourself.