The modulus of the complex number z such that |z+3-i|=1 and (z)= is equal to

Step-by-step solution

Let z=x+i y Given, |z+3-i|=1 aligned & |(x+3)+(y-1) i|=1 & (x+3)^2+(y-1)^2 =1 & (x+3)^2+(y-1)^2=1 (i) aligned Above is the equation of circle with centre (-3,1) and radius =1 Also, (z)= ⁻¹ | y x |= | y x |= =0 y=0 By Eq. (i), aligned & x & =-3 & z & =-3+0 i & Modulus of z & =3 aligned