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The locus of point z satisfying Re(z^(2)...

The locus of point z satisfying Re`(z^(2))=0`, is

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Let z_1=3 and z_2=7 represent two points A and B respectively on complex plane . Let the curve C_1 be the locus of pint P(z) satisfying |z-z_1|^2 + |z-z_2|^2 =10 and the curve C_2 be the locus of point P(z) satisfying |z-z_1|^2 + |z-z_2|^2 =16 The locus of point from which tangents drawn to C_1 and C_2 are perpendicular , is :