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GATE 2024 IN – Question 11

Engineering Mathematics · Complex variables · 1 mark · Multiple choice

Let $z=x+iy$ be a complex variable and $\bar z$ its complex conjugate. The equation $\bar z^2+z^2=2$ represents a

  1. parabola
  2. hyperbola
  3. ellipse
  4. circle

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Show answer and explanation

Correct answer: (B) hyperbola

Explanation

Expand $z^2=(x+iy)^2=x^2-y^2+2ixy$ and $\bar z^2=x^2-y^2-2ixy$. Their sum is $2(x^2-y^2)=2$, so $x^2-y^2=1$, a **hyperbola, B**.