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in Mathematics by (66.1k points)

A function f is defined on the complex number by f(z) = (a + bi)z, where ‘a’ and ‘b’ are positive numbers. This function has the property that the image of each point in the complex plane is equidistant from that point and the origin. Given that |a + bi| = 8 and that b2 = u/v where u and v are co-primes. Find the value of (u + v).

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Best answer

 f(z) = (a + ib)(Z) = c + id

Z = (x + iy)

Image = c – id

(c – x)2 + (y + d)2 = c2 + d2

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