Question

How do you write the complex number in trigonometric form `sqrt3+i`?

Answer 1

For a number of form, `a + bi`, the form `A(cos(theta) + isin(theta))` is obtained by using `A = sqrt(a² + b²` and `theta = tan^-1(b/a)` (adjust `theta` for the proper quadrant)

Explanation:

`A = sqrt(sqrt3^2 + 1^2`

`A = 2`

`theta = tan^-1(1/sqrt3)`

`theta = pi/6`

Because the signs of "a" and "b" are positive, we do not adjust the quadrant.

`sqrt3 + i = 2(cos(pi/6) + isin(pi/6))`