To finish this problem it is best to use number notation.
.
Now real numbers have arguments that are integral multiples of pi
So the second answer is n=6.
Express the comlex number (√3+i) in trigonometric form. Hence find the smallest positive integer n that (√3+i)^n is a real number.
This is how I have started it however im really not sure if this is right hoping someone could help.
ArgZ = tan^-1 (1/√3) = 30
|Z| = √3+1 = 2
Z = 2(cos30+isin30)
Is this correct??
Also how do i complete the question??
Thanks
still on the topic of complex numbers, could anybody tell me if this is correct?
complex number Z and conjugate Zbar satisfy equation
3Z + Zbar = (11+7i)/(1+i)
find Z in form x + iy
This is how i attempt to answer it but unsure if its correct
let Z = x + iy
Zbar = x - iy
3(x+iy) + (x-iy) = (11+7i)/(1+i)
3 (x+iy) + (x-iy) = 10 + 6i
2(x + iy) = 10 + 6i
(x+iy) = (10 + 6i))/2
x + iy = 5 + 3i
is this correct anybody please???