(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Finding the angle without a calculator (CA)

**Physics Forums | Science Articles, Homework Help, Discussion**