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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.
Please feel free to post as many doubts on our discussion forum as you can. If you find any questionDifficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best Prashant!!!Regards,Askiitians ExpertsPriyansh Bajaj
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