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rachneet kaur Grade:
        

if ABC is an equilateral triangle then if A and B are denoted by complex nos z1 and z2 then C is denoted by z3 =z1 e^-i(pi\3)+z2 e^i(pi\3).

6 years ago

Answers : (1)

AskiitiansExpert Mohit-IITD
21 Points
										

Dear Rachneet,


z3-z2=(z2-z1)ei2π/3 (Rotating vector z2-z1 by external angle 2π/3 to get vector z3-z2)


z3=(1+ei2π/3)z2-z1ei2π/3 


Now, 1+ei2π/3=-ei4π/3 (using 1+ω=-ω2) and -1=e-iπ 


so 1+ei2π/3=-ei4π/3=ei(4π/3-π)=eiπ/3 


also -ei2π/3=ei(2π/3-π)=e-iπ/3


z3=(1+ei2π/3)z2-z1ei2π/3 =>z3=z1e-iπ/3+z2eiπ/3 


Hence proved.


Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation. 


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6 years ago
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