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You need to convert the given algebraic form of complex number `z = -2 + 2sqrt3*i` to the polar form `z = r*e^(i*theta)` , using Euler's formula `e^(i*theta) = cos theta + i*sin theta` .
You need to make the conversion from cartesian coordinates `(x,y)` of complex number `z = x + i*y` into polar coordinates `(r, theta)` , where r represents the magnitude of z and `theta` is the angle between the position vector bar z and x axis, such that:
`r = |z| = sqrt(x^2 + y^2)`
`theta = tan^(-1) (y/x)`
Identifying `x = -2, y = 2sqrt3` , yields:
`r = sqrt(4 + 12) => r = sqrt 16 => r = 4`
`theta = tan^(-1)(2sqrt3/(-2)) => theta = tan^(-1)(-sqrt3)`
`theta = -tan^(-1)(sqrt3) =>tan theta = -sqrt3 =>theta = pi - pi/3 => theta = (2pi)/3`
`e^(i*(2pi)/3) = cos ((2pi)/3) + i*sin ((2pi)/3)`
Hence, converting the given algebraic form of the complex number to the polar form `re^(i*theta)` yields `-2 + 2sqrt3*i = 4*e^(i*(2pi)/3).`
I wanna change to the second form.
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