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प्रश्न
Find z if |z| = 4 and arg(z) = `(5pi)/6`.
उत्तर
Given that: |z| = 4 and arg(z) = `(5pi)/6`
⇒ θ = `(5pi)/6`
|z| = 4
⇒ r = 4
So Polar form of z = `r[cos theta + i sin theta]`
= `4[cos (5pi)/6 + i sin (5pi)/6]`
= `4[cos (pi - pi/6) + i sin(pi - pi/6)]`
= `4[- cos pi/6 + i sin pi/6]`
= `4[(-sqrt(3))/2 + i 1/2]`
= `-2sqrt(3) + 2i`
Hence z = `-2sqrt(3) + 2i`.
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