WBJEE · Maths · Complex Number
In the argand plane, the distinct roots of \(1+z+z^{3}+z^{4}=0(z\) is a complex number) represent vertices of
- A a square
- B an equilateral triangle
- C a thombus
- D a rectangle
Answer & Solution
Correct Answer
(B) an equilateral triangle
Step-by-step Solution
Detailed explanation
Given equation is \(1+z+z^{3}+z^{4}=0\) \(\Rightarrow \quad(1+z)+z^{3}(1+z)=0\) \(\Rightarrow \quad(1+z)\left(1+z^{3}\right)=1\) \(\Rightarrow \quad z=-1, z^{3}=-1\) \(\Rightarrow \quad z=-1, z=-1,-\omega-\omega^{2}\) Hence, these roots are the vertices of an equilateral…
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