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Question
The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.
Options
|z|2
`|barz|^2`
`|z|^2/2`
None of these
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Solution
The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is `underlinebb(|z|^2/2)`.
Explanation:
Let z = x + iy.
Then –iz = y – ix.
Therefore, z + iz = (x – y) + i(x + y)
Required area of the triangle = `1/2(x^2 + y^2) = |z|^2/2`.
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