Algebra

Complex Numbers

Complex Numbers - Argand Plane

         

Suppose that we have two complex numbers z1=32iz_1 = 3 - 2i and z2=43iz_2 = 4 - 3i.

In what quadrant is this complex number z1z2z_1z_2 located?

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

In units2 \text{units}^2, what is the area of the rectangle formed by the vertices 2+3i,4+2i,i2 + 3i, 4 + 2i, -i, and 22i2 - 2i?

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

Which function represents this transformation?

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

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