AP EAMCET · Maths · Complex Number
Area of the triangle formed by the complex numbers \(\mathrm{z}, \mathrm{iz}\) and \(\mathrm{z}+\mathrm{iz}\) in the Argand diagram as vertices is
- A \(\frac{1}{2} \cdot|z|^2\)
- B \(\frac{1}{2} \cdot z^2\)
- C \(\mathrm{z}^2\)
- D \(|z|^2\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2} \cdot|z|^2\)
Step-by-step Solution
Detailed explanation
Let \(Z=x+i y ; i z=-y+i x\) and \(\mathrm{Z}+\mathrm{iz}=(\mathrm{x}-\mathrm{y})+\mathrm{i}(\mathrm{x}+\mathrm{y})\) \(\therefore\) Area of triangle…
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