OpenStax-CNX module: m49408
Polar Form of Complex Numbers
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In this section, you will:
Plot complex numbers in the complex plane.
Find the absolute value of a complex number
Write complex numbers in polar form.
Convert a complex number from polar to rectangular form.
Find products of complex numbers in polar form.
Find quotients of complex numbers in polar form.
Find powers of complex numbers in polar form.
Find roots of complex numbers in polar form.
God made the integers; all else is the work of man. This rather famous quote by nineteenth-century
German mathematician Leopold
sets the stage for this section on the polar form of a complex
Complex numbers were invented by people and represent over a thousand years of continuous
investigation and struggle by mathematicians such as
, De Moivre,
Complex numbers answered questions that for centuries had puzzled the greatest minds in
We rst encountered complex numbers in Complex Numbers.
In this section, we will focus on the
mechanics of working with complex numbers: translation of complex numbers from polar form to rectangular
form and vice versa, interpretation of complex numbers in the scheme of applications, and application of De
1 Plotting Complex Numbers in the Complex Plane
a + bi
is similar to plotting a real number, except that the horizontal axis
represents the real part of the number,
and the vertical axis represents the imaginary part of the number,
Given a complex number
plot it in the complex plane.
a + bi,
how to feature:
1.Label the horizontal axis as the real axis and the vertical axis as the imaginary axis.
2.Plot the point in the complex plane by moving
units in the horizontal direction and
in the vertical direction.
Plotting a Complex Number in the Complex Plane
Plot the complex number
Version 1.2: Jul 8, 2014 10:00 am +0000