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PRASHANT MISHRA Grade:
        

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

6 years ago

Answers : (2)

mycroft holmes
270 Points
										

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

6 years ago
Priyansh Bajaj AskiitiansExpert-IITD
30 Points
										

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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Priyansh Bajaj

6 years ago
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