TS EAMCET · Maths · Complex Number
If \(z=x+i y\) satisfies the equation \(z^2+a z+a^2=0, a \in \mathbb{R}\), then
- A \(|z|=|a|\)
- B \(|z-a|=|a|\)
- C \(z=|a|\)
- D \(z=a\)
Answer & Solution
Correct Answer
(A) \(|z|=|a|\)
Step-by-step Solution
Detailed explanation
\(z=x+i y\) Put in \(z^2+a z+a^2=0\) \(\begin{aligned} & \Rightarrow x^2-y^2+2 i x y+a x+i y+a^2=0 \\ & \Rightarrow x^2-y^2+a x+a^2+i(2 x y+a y)=0 \end{aligned}\) Comparing imaginary part \(2 x y+a y=0 \Rightarrow x=\frac{-a}{2} \quad[\because y \neq 0]\) Comparing real part ;…
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