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What is the maximum value of ∣z∣|z|∣z∣ if z is a complex number satisfying ∣z+2z∣=2|z+\dfrac{2}{z}|=2∣z+z2∣=2
Details :
∙\bullet∙ If z=a+i.bz=a+i.bz=a+i.b is a complex number with a,b∈Ra,b \in Ra,b∈R and i=−1i=\sqrt{-1}i=−1, then ∣z∣=a2+b2|z|=\sqrt{a^2+b^2}∣z∣=a2+b2
∙\bullet∙ Answer after rounding off up to 3 decimal places.
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