Solving polar form complex number
The polar form of a complex number is a way of expressing a complex number in terms of its magnitude (or absolute value) and its argument (or phase). It is typically written in the form:
z = r * cis(θ)
where r is the magnitude of the complex number, cis(θ) is the complex number in polar form, and θ is the argument of the complex number in radians.
Here are five examples of how to express a complex number in polar form:
Example 1:
Express the complex number 3 + 4i in polar form.
Solution:
The magnitude of the complex number 3 + 4i is 5, and the argument is 53.13 degrees. Therefore, the polar form of the complex number is:
z = 5 * cis(53.13 degrees)
Example 2:
Express the complex number -4 + 3i in polar form.
Solution:
The magnitude of the complex number -4 + 3i is 5, and the argument is 126.87 degrees. Therefore, the polar form of the complex number is:
z = 5 * cis(126.87 degrees)
Example 3:
Express the complex number -1 - 2i in polar form.
Solution:
The magnitude of the complex number -1 - 2i is 2.236, and the argument is -63.43 degrees. Therefore, the polar form of the complex number is:
z = 2.236 * cis(-63.43 degrees)
Example 4:
Express the complex number -3 - 4i in polar form.
Solution:
The magnitude of the complex number -3 - 4i is 5, and the argument is -53.13 degrees. Therefore, the polar form of the complex number is:
z = 5 * cis(-53.13 degrees)
Example 5:
Express the complex number 4 - 3i in polar form.
Solution:
The magnitude of the complex number 4 - 3i is 5, and the argument is -126.87 degrees. Therefore, the polar form of the complex number is:
z = 5 * cis(-126.87 degrees)