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  • Answer please! - Complex numbers and quadratic equations - JEE Main-8

A\left ( z_{1} \right ),B\left ( z_{2} \right ),O\left ( o \right ) are vertices of right angled isosceles triangle , right angled at O then z_{1}^{2}+z_{2}^{2}  equals 

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verify Rotation on \angle AOB

\frac{Z_{i}-0}{Z_{2}-0}=\frac{\left | Z_{1}-0 \right |}{\left | Z_{2}-0 \right |}\left ( \cos \frac{\pi }{2} +i\sin \frac{\pi }{2}\right )

\Rightarrow \frac{Z_{1}}{Z_{2}}=\frac{OA}{OB}\propto i

\Rightarrow Z_{1}=iZ_{2}

\Rightarrow Z_{1}^{2}+Z_{2}^{2}=0

 

Rotation -

\frac{z_{3}-z_{1}}{z_{2}-z_{1}}=\frac{\left |z_{3}-z_{1} \right |}{\left |z_{2}-z_{1} \right |}.e^{i\Theta }

 

 

- wherein

e^{i \theta}=\cos \theta+i\sin \theta

 

 


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