Question

In these complex exponential problems, solve for x:

1)e^(i*pi) + 2e^(i*pi/4)=?

2)3+3=3i*sqrt(3)=xe^(i*pi/3)


MY attempt:

I'm not really sure of what they are asking.
For the 1st one I used the e^ix=cos(x)+i*sin(x)
and got -1+sqrt(2) +sqrt(2)i

2) I solved for x and fot (3+3i*sqrt(3))/(1/2+i*sqrt(3)/2)

Answer 1

your 1st answer is correct

#2.
x(1/2 + √3/2 i) = 3+3i√3
x = (3+3√3 i))/[1/2 (1+√3 i)]

now rationalize by multiplying by conjugate

x = 3(1+√3 i)* 2(1-√3 i)/(1-3)
x = -3(1+√3 i))(1-√3 i)
x = -3(1-3)
x = 6