JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(a \neq b\) be two non-zero real numbers.Then the number of elements in the set \(X =\left\{ z \in C : \operatorname{Re}\left(a z^2+ bz \right)= a \text { and }\operatorname{Re}\left(b z^2+ az \right)= b \right\}\) is equal to
- A \(1\)
- B \(3\)
- C \(0\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(0\)
Step-by-step Solution
Detailed explanation
\(\operatorname{Re}\left(a z^2+b z\right)=a\) \(a z^2+b z+a \bar{z}^2+b \bar{z}=2 a\) \(a\left(z^2+\bar{z}^2\right)+ b ( z +\overline{ z })=2 a\) \(\operatorname{Re}\left( bz z^2+ az \right)= b\) \(b z^2+a z+b \bar{z}^2+ az =2 b\)…
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