Question

How do you convert `(sqrt 3) + i` to polar form?

Answer 1

`sqrt3+i` in polar form is written as `2cos(pi/6)+2isin(pi/6)` or `2e^(i(pi/6)`

Explanation:

Complex number `a+ib` is written as `rcostheta+irsintheta` or `re^(itheta)` in polar form.

where, `r=sqrt(a^2+b^2)3 and`tantheta=b/a`or`theta=arctan(b/a)#

Hence for `sqrt3+i`

`r=sqrt((sqrt3)^2+1^2)=sqrt4=2` and `theta=arctan(1/sqrt3)=pi/6`

Hence `sqrt3+i` in polar form is written as `2cos(pi/6)+2isin(pi/6)`

or `2e^(i(pi/6)`