Question

CAN SOMEONE PLS HELP MEE

Answer 1

`4√(3) - 4i = \boxed{\left(8, (\pi)/(6)\right)}`

Explanation:

Given complex number is:
To plot this on polar coordinates use the fact that a complex number of the form
`z=x+yi` can be converted to polar form
`(r, \theta)` using the relationship

`r = √(x^2 +y^2) )\\\mathrm{and}\\\theta = cos^(-1)\left((x)/(r)}\right)`

Comparing
`4√(3) - 4i` and
`z=x+yi`

we see that

`r = \sqrt{(4√(3))^2 + (-4)^2}\\\\r = √(48 + 16)\\\\\\r = √(64) = 8\\\\\theta = cos^(-1) \left((4√(3))/(8)\right)`

`\theta = \cos^(-1) \left((√(3))/(2)\right) = 30^\circ = (\pi)/(6) \;radians`

So in polar coordinates,

`4√(3) - 4i = \left(8, (\pi)/(6)\right)`