If -z-2 and z-4- find z-

Let z=r (cos θ+i sin θ) |z|=r=2 and θ=π/4 z=2[cosπ/4+i sinπ/4 ] [∵ z=r (cosθ+i sinθ)] =2[1/√(2)+i 1/√(2) ] =√(2)(1+i) ...

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Polar Representation of a Complex Number

If |z|=2 and ...

Question

$If | z | = 2 and a r g (z) = \frac{π}{4}, find z .$

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z_{2}

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If |z| = 4 and arg z = - $\frac{π}{4}$ , then z is:

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⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{3 π}{4} & w h e n & | z | \leq | z - 2 | \frac{- π}{4} & w h e n & | z | > | z - 4 | \end{matrix}

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