Question

How do you multiply `e^(( 13 pi )/ 8 i) * e^( pi/2 i )` in trigonometric form?

Answer 1

Just do the conversion and then multiply as you did back in Algebra I:
`e^((13pi)/8i)=cos((13pi)/8)+i*sin((13pi)/8)`
`e^(pi/2i)=cos (pi/2) + i*sin (pi/2)=i`

`(cos((13pi)/8)+i*sin((13pi)/8))*i=-sin((13pi)/8)+cos((13pi)/8)i`