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Complex Numbers

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?

Quadrant I Quadrant II Quadrant III Quadrant IV

by Brilliant Staff

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

Line Parabola Square Circle

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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 $2 - 2i$ ?

by Brilliant Staff

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

Which function represents this transformation?

f(z) = -z

f(z) = \bar{z}

f(z) = z^2

f(z) = iz

by Brilliant Staff

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

Real axis Origin First Quadrant Imaginary axis

by Brilliant Staff

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