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The greatest positive agrument of complex no. satisfyinh |z-4|=Re(z) is __

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\begin{array}{l} |z-4|=\operatorname{Re}(z) \\ \Rightarrow \sqrt{(x-4)^{2}+y^{2}}=x \\ \text { or } x^{2}-8 x+16+y^{2}=x^{2} \\ \text { or } y^{2}=8(x-2) \end{array}

The given relation represents the part of the parabola with focus (4,0) lying above the x−axis and the imaginary axis as the directrix. The two tangents from directrix are at right angle. Hence, greatest positive argument of z is \frac {\pi}{4}

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Deependra Verma

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