find the no of complex numbers satisfying |z|=z+1+2i - Maths - Complex Numbers and Quadratic Equations

Question

find the no of complex numbers satisfying |z|=z+1+2i

Priyanka Kedia · Accepted Answer

Let, z=x+iy where x and y are real numbers
So,z=z+1+2i⇒x2+y2=x+iy+1+2i⇒x2+y2=x+1+iy+2On comparing the real and imaginary parts, we have,y+2=0⇒y=-2And,x2+y2=x+1⇒x2+4=x+1        put y=-2Squaring on both side,x2+4=x2+1+2x⇒2x=3⇒x=32Thusz=32-2i is the solution of given equation

find the no. of complex numbers satisfying |z|=z+1+2i