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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.
(−4, 2) ←→ z = −4 + 2i 3i
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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