Complex Numbers

Suppose that we have two complex numbers \(z_1 = 3 - 2i\) and \(z_2 = 4 - 3i\). In what quadrant is this complex number \(z_1z_2\) located?

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What is the shape of graph of the equation \(\left|z\right| = 4\) in the complex plane?

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In \( \text{units}^2\), what is the area of the rectangle formed by the vertices \(2 + 3i, 4 + 2i, -i\), and \(2 - 2i\)?

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Suppose the function \(f(z)\) takes the complex number \(z\) and rotates it 90 degrees counterclockwise around the origin.

Which function represents this transformation?

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For a complex number \(z\), on which part of the Argand plane does \(\text{Re}(z) + \text{Im}(iz)\) sit?

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Argand Plane