If the complex numbers z (1) , z (2) and...

If the complex numbers `z _(1) , z _(2) and z _(3)` denote the vertices of an isosceles triangle, right angled at `z _(1),` then `(z _(1) - z _(2)) ^(2) + (z _(1) - z _(3)) ^(2)` is equal to A)0 B)`(z _(2) + z _(3)) ^(2)` C)2 D)3

A

0

B

`(z _(2) + z _(3)) ^(2)`

C

2

D

3

Verified by Experts

The correct Answer is:

A

Similar Questions

Explore conceptually related problems

If z_(1)=2+3i and z_(2)=3+2i , then |z_(1)+z_(2)| is equal to

If z = e ^( 2pi l 3) , then 1 + z + 3z ^(2) + 2z ^(3) + 2z ^(4) + 3z ^(5) is equal to

If z _(1) = 2 sqrt2 (1 + i) and z _(2) = 1 + isqrt3, then z _(1) ^(2) z _(2) ^(3) is equal to

Let z_(1) = 3 + 4i and z_(2) = - 1 + 2i . Then, |z_(1) + z_(2)|^(2) - 2(|z_(1)|^(2) + |z_(2)|^(2)) is equal to

If z= 2- isqrt(3) then |z^(4)| is equal to

Consider the complex number z_1 = 3+i and z_2 = 1+i .Find 1/z_2

Let z _(1) = 1 + i sqrt3 and z _(2) = 1 + i, then arg ((z _(1))/( z _(2))) is

If z = (2-i)/(i) , then R e(z^(2)) + I m(z^(2)) is equal to a)1 b)-1 c)2 d)-2

If (2 z _(1))/(3z _(2)) is a purely imaginary, then | ( z _(1) - z _(2))/( z _(1) + z _(2))| is: