Stitz-Zeager_College_Algebra_e-book

To do so we choose to solve the equation y 2t 1 for t

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Unformatted text preview: f 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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