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PhysicsMark

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## 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.