1.3 Complex Numbers, Complex Numbers

Powers of i

Example: Simplify the power of i.

i^-59

Solution:

i^-59

Rewrite the exponential expression with negative exponents by using the reciprocal property.

=1/{i^59}

Simplify the i^59 by dividing 59 by 4.  The remainder will tell you which position in the pattern you are in.  59 divided by 4 is 14 with a reminder of 3.

=1/{i^3}

=1/{-i}

=1/{-i}  {i /i}

=i/{-i^2}

=i/{-(-1)}

=i/{1}

=i