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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.

# Complex Numbers - 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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