`Z_1!=Z_2` are two points in an Argand plane. If `a|Z_1|=b|Z_2|,` then prove that `(a Z_1-b Z_2)/(a Z_1+b Z_2)` is purely imaginary.

Z_(1)!=Z_(2) are two points in an Argand plane.If a|Z_(1)|=b|Z_(2)|, then prove that (aZ_(1)-bZ_(2))/(aZ_(1)+bZ_(2)) is purely imaginary.

Let z_1 nez_2 are two points in the Argand plane if a abs(z_1)=b abs(z_2) then point (az_1-bz_2)/(az_1+bz_2) lies

Prove that |z_1+z_2|^2=|z_1|^2, ifz_1//z_2 is purely imaginary.

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

z_1a n dz_2 are two distinct points in an Argand plane. If a|z_1|=b|z_2|(w h e r ea ,b in R), then the point (a z_1//b z_2)+(b z_2//a z_1) is a point on the (a)line segment [-2, 2] of the real axis (b)line segment [-2, 2] of the imaginary axis (c)unit circle |z|=1 (d)the line with a rgz=tan^(-1)2

z_1a n dz_2 are two distinct points in an Argand plane. If a|z_1|=b|z_2|(w h e r ea ,b in R), then the point (a z_1//b z_2)+(b z_2//a z_1) is a point on the line segment [-2, 2] of the real axis line segment [-2, 2] of the imaginary axis unit circle |z|=1 the line with a rgz=tan^(-1)2

z_1a n dz_2 are two distinct points in an Argand plane. If a|z_1|=b|z_2|(w h e r ea ,b in R), then the point (a z_1//b z_2)+(b z_2//a z_1) is a point on the line segment [-2, 2] of the real axis line segment [-2, 2] of the imaginary axis unit circle |z|=1 the line with a rgz=tan^(-1)2

Given that |z_1+z_2|^2=|z_1|^2+|z_2|^2 , prove that z_1/z_2 is purely imaginary.

Prove that |z_1+z_2|^2 = |z_1|^2 + |z_2|^2 if z_1/z_2 is purely imaginary.