AP EAMCET · Maths · Complex Number
If the roots of the equation \(Z^3+i Z^2+2 i=0\) are the vertices of a triangle \(A B C\). then that triangle \(A B C\) is
- A a right angled triangle
- B an equilateral triangle
- C an isosceles triangle
- D a right angled isosceles triangle
Answer & Solution
Correct Answer
(C) an isosceles triangle
Step-by-step Solution
Detailed explanation
Given, \(Z^3+i Z^2+2 i=0\) \(\begin{aligned} & \Rightarrow(Z-i)\left(Z^2+2 i Z-2\right)=0 \\ & Z=i \text { or } Z^2+2 i Z-2=0 \\ & \Rightarrow Z=\frac{-2 i \pm 2}{2} \Rightarrow z=-i+1,-i-1 \end{aligned}\) Let \(A(0,1), B(1,-1), C(-1,-1)\) \(A B=\sqrt{5} ; B C=2 ; A C=\sqrt{5}\)…
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