Question

Simplify 1+i over 1-i I'll draw it in the answer section.

Answer 1

\[\frac{1+i}{1-i}=\frac{1+i}{1-i}\times \frac{1+i}{1+i}\] multiply by the conjugate of the denominator

Answer 2

I did that and got a fraction and the answer is a whole number. I don't have the work with me anymore though

Answer 3

reason this works is that
\[(a+bi)(a-bi)=a^2+b^2\] a real number so your denominator will be \[1^2+1^2=2\] your numerator is whatever you get when you multiply

Answer 4

numerators is
\[(1+i)(1+i)=1+2i-1=2i\] so answer is
\[\frac{2i}{2}=i\]

Answer 5

Okay thank you!