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Question
Select the correct answer from the given alternatives:
If `-1 + sqrt(3)"i"` = reiθ , then θ = .................
Options
`-(2pi)/3`
`pi/3`
`-pi/3`
`(2pi)/3`
Solution
`(2pi)/3`
Explanation;
reiθ = `-1 + "i"sqrt(3)`
= `2((-1)/2 + "i"sqrt(3)/2) ...[("a" = (-1)/2),("b" = sqrt(3)/2)]`
= `2[cos(pi - pi/3) + "i"sin (pi - pi/3)]`
= `2(cos (2pi)/3 + "i"sin (2pi)/3)`
∴ θ = `(2pi)/3`.
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