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z , denoted Re(z ), while the real number b is called the imaginary part of z , denoted Im(z ). From
Intermediate Algebra, we know that if z = a + bi = c + di where a, b, c and d are real numbers,
then a = c and b = d, which means Re(z ) and Im(z ) are well-deﬁned.1 To start oﬀ this section,
we associate each complex number z = a + bi with the point (a, b) on the coordinate plane. In
this case, the x-axis is relabeled as the real axis, which corresponds to the real number line as
usual, and the y -axis is relabeled as the imaginary axis, which is demarcated in increments of the
imaginary unit i. The plane determined by these two axes is called the complex plane.
Imaginary Axis
4i
(−4, 2) ←→ z = −4 + 2i 3i
2i
i (3, 0) ←→ z = 3 01
−4 −3 −2 −1
−i 2 3 4 Real Axis −2i
−3i (0, −3) ←→ z = −3i −4i The Complex Plane
Since the ordered pair (a, b) gives the rectangular coordinates associated with the complex number
z = a + bi, the expression z = a + bi is called the rectangular form of z . Of course, we could just
as easily associate z with a pai...

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