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Complex Numbers

"Complex" numbers share many properties with the real numbers. In fact, complex numbers include all the real numbers, so you know lots of them already. Such an overachiever.

Argand Plane

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?

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

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

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

Which function represents this transformation?

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

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