# If Z1 and Z2 are two complex nos. such that Z1+Z2i=Z2 THEN origin, Z1 and Z2 r the vertices of a___________________ TRIANGLE?

mycroft holmes
272 Points
13 years ago

The lengths of the three sides of the triangle are

We see that

Also,

This also tells us that

Hence the triangle is a right angled isoceles triangle

30 Points
13 years ago

Dear Prashant,

Solution:- z1 + z2 i = z2

or, z2 - z1  = i z2

or, (z2 - z1) / (z2 - 0) = i ['0' is written to represent origin]

or, (z2 - z1) / (z2 - 0) = e(i∏/2) [|z2 - z1| / |z2 - 0|]; where,|z2 - z1| = |z2 - 0| and

therefore,[|z2 - z1|/|z2 - 0|] =1

Hence, origin, z1 and z2 are the vertices of isosceles right angled triangle, having right angle between (z2 - z1) and (z2 - origin) sides.

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