AP EAMCET · Maths · Complex Number
If the vertices \(A, B\) and \(C\) of an isosceles \(\triangle A B C\) are respectively \(z_1, z_2\) and \(z_3\) and if \(\angle C=90^{\circ}\), then
- A \(\left(z_1-z_2\right)=\left(z_1-z_3\right)\left(z_3-z_2\right)\)
- B \(\left(z_1-z_2\right)^2=\left(z_1-z_3\right)\left(z_3-z_2\right)\)
- C \(\left(z_1-z_2\right)^2=2\left(z_1-z_3\right)\left(z_3-z_2\right)\)
- D \(z_1^2+z_2^2+z_3^2=z_1 z_2 z_3+2\)
Answer & Solution
Correct Answer
(C) \(\left(z_1-z_2\right)^2=2\left(z_1-z_3\right)\left(z_3-z_2\right)\)
Step-by-step Solution
Detailed explanation
\(\triangle A B C\) is an isosceles right angled triangle with \(A B\) as hypotenuse. \[ \frac{z_1-z_2}{z_3-z_2}=\sqrt{2} e^{i \pi / 4} \] [Apply rotation about a point \(B\) ]…
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