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If z is a complex number such that |z|=2...

If z is a complex number such that `|z|=2`, then the area (in sq. units) of the triangle whose vertices are given by `z, -iz and iz-z` is equal to

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To find the area of the triangle with vertices at \( z \), \( -iz \), and \( iz - z \), where \( |z| = 2 \), we can follow these steps: ### Step 1: Express \( z \) in terms of its components Let \( z = x + iy \), where \( x \) and \( y \) are real numbers. Given that \( |z| = 2 \), we have: \[ |z| = \sqrt{x^2 + y^2} = 2 \] Squaring both sides gives: \[ x^2 + y^2 = 4 \]
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