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

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

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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