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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 = `pi/3`
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Solution
Let 2 – 2i
Modules = |z| = `sqrt(2^2 + 2^2)`
= `2sqrt(2)`
Argument θ = `tan^-1 ((-2)/2)`
= `tan^-1 (- 1)`
= `- pi/4`
When ‘z’ is rotated in the counter clockwise direction about the origin when θ = `pi/3`
i.e., Argument of new position
= `pi/3 - pi/4`
= `pi/12`
∴ New position is `2sqrt(2) (cos pi/12 + "i" sin pi/12)`
= `2sqrt(2) "e"^(("i"pi)/12)`
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