Write z = 9 - 3 sqrt 3i in polar form. you so !

z = 6√3(cos(11π/6)+isin(11π/6))

Step-by-step explanation:

We have given an equation in complex form.

z = 9-3√3i

z = a+bi is general form of comple number.

on comparing above two equations, we get

a = 9   and b = -3√3

We have to write it in polar form.

The formula to convert an equation in ploar form is:

z = r(cos∅+isin∅)    where r is magnitude of z and ∅ is angle.

r = √a²+b²   and ∅ = tan⁻¹(b / a)

putting the values of a and b in above two formulas , we have

r = √(9)²+(-3√3)² = √81+27 = √108 = √36×3 = 6√3

∅ = tan⁻¹(-3√3 / 9)

∅ =  tan⁻¹(-1/√3)

∅ = -π / 6

we have to change ∅ in positive.

∅ = 2π-π/6 = 12π-π / 6

∅ = 11π / 6

putting the value of r and ∅ in given formula, we get

z = 6√3(cos(11π/6)+isin(11π/6)) is the polar form of given complex number.

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