1.

Convert of the complex number in the polar form: `sqrt(3)+i`

Answer» Here, `z = -sqrt(3) + i`
Comparing it with polar form, we get,
`rcostheta = sqrt3 and rsintheta = 1`
Squaring and adding these two terms, we get,
`r^2cos^2theta+r^2sin^2theta = 4 `
`r^2(cos^2theta+sin^2theta) = 4`
`r^2 = 4=> r = 2`
So, modulus `|r|` is `2`.
Now, `rsintheta = 1=>sintheta = 1/2`
`theta = pi/6`
As `costheta` is positive and `sintheta` is positive, theta lies in first quadrant.
So, `theta = pi/6`
Polar form, `z = 2(cospi/6+isinpi/6)`


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