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Question
If z = 2 – 2i, find the rotation of z by θ radians in the counterclockwise direction about the origin when θ = `(2pi)/3`
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Solution
Let 2 – 2i
Modules = |z| = `sqrt(2^2 + 2^2)`
= `2sqrt(2)`
Argument θ = `-1 ((-2)/2)`
= `tan^-1 (- 1)`
= `- pi/4`
θ = `(2pi)/3`
∴ Argument = `(2pi)/3 - pi/4`
= `(5pi)/12`
∴ New position is `2sqrt(2) (cos (5pi)/2 + "i" sin (5pi)/12)`
= `2sqrt(2) "e"^((15pi)/12)`
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