|z-3-4i|=7 find the locus of z. sol.we know that in argand plane the complex no. is represented with a pt. compare this equation with |z-q|=r whera q is a complex no. (every real no. is also a complex no.)so Q=(3,4) in argand plane .and z is any point on the argand plane. |z-3-4i| represent the distance of point z from pt.(3,4) in the argand plane or complex plane. this distance is also given in the question =7.so the locus of z is any point from pt.(3,4) which is at a distance 7 from point (3,4).which is represnt a circle.because the circle is a curve traced by a moving point which is moving in such a way that it is at a fixed distance from a fixed pt. while moving.

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It can be re written in Cartesian form as (x-3)^2 + (y-4)^2 = 7^2 This is equation of a circle with center at (3,4) and radius equal to 7
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Mathematics for JEE Mains/Advanced, XI & XII (All Boards)

Circle (3,4);7
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Solution: Let z = x +iy I x+iy -3 -4i I= 7 I (x-3) +(y-4)i I = 7 (x-3)^2 +(y-4)^2 = 7^2 is the locus of Z. which is a circle with center at( 3, 4) and radius 7 units.
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(x-3)^2 + (y-4)^2 = 7^2
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