How do you simplify i^59i59?

3 Answers
Monzur R.
Jun 30, 2018

i^59=-ii59=−i

Explanation:

i^59=i^56i^3=(i^16)^4i^3=1i^3=i^2i=-ii59=i56i3=(i16)4i3=1i3=i2i=−i

Jacobi J.
Jun 30, 2018

-i−i

Explanation:

Recall that

i^2=-1i2=−1

i^3=-ii3=−i

i^4=1i4=1 (Any multiple of 44 exponent will also be 11)

With this in mind, we can rewrite i^59i59, since the exponent is a prime number.

i^59=color(blue)(i^56)*i^3i59=i56⋅i3

Since 5656 is a multiple of 44, i^56=1i56=1. What we have simplifies to:

1*i^3=-i1⋅i3=−i

Hope this helps!

Ratnaker Mehta
Jun 30, 2018

i^59=i^59xxi^2/i^2={(i^60)(i)}/(-1)=(i^4)^15*i/-1=1^15*-i=-ii59=i59×i2i2=(i60)(i)−1=(i4)15⋅i−1=115⋅−i=−i.

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