- #1
PhysicsMark
- 91
- 0
Homework Statement
In my math class, we are not permitted to use a calculator. I am currently reviewing for a test and came across a small problem.
Perform the following operation using the Euler (polar) form for the complex numbers involved.
(1-3i)/i
Homework Equations
The Attempt at a Solution
I know of 2 ways to write the numerator in polar form. Both depend on knowing the argument, or angle.
1. (1-3i) = [tex]\sqrt{10}(cos{\theta}+i{sin{\theta}})[/tex]
2. (1-3i)= [tex]\sqrt{10}e^{i\theta}[/tex]
Performing the actual operation either in cartesian or Euler/polar form is not difficult for me. However I cannot think of how to find theta without a calculator.
Is the 1, 3, [tex]\sqrt{10}[/tex] triangle a special triangle that I should have memorized?
Like the 1, [tex]\sqrt{3}[/tex], 2 triangle with angle 60, or pi/3.