The points `9 +i,4 + 13i,-8 + 8i.-3-4i` in the Argand diagram represent

Two points P and Q in the Argand diagram represent z and 2z+3+i. If P moves on a circle with centre at the origin and radius 4, then the locus of Q is a circle with centre

Draw argand diagram of 6+2i.

Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)), and i as vertices in the Argand diagram is isosceles.

Let 3-i and 2+i be affixes of two points A and B in the Argand plane and P represents the complex number z=x+iy . Then, the locus of the P if |z-3+i|=|z-2-i| , is