Finding the angle without a calculator (CA)

[PhysicsMark]

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) = \sqrt{10}(cos{\theta}+i{sin{\theta}})

2. (1-3i)= \sqrt{10}e^{i\theta}

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, \sqrt{10} triangle a special triangle that I should have memorized?

Like the 1, \sqrt{3}, 2 triangle with angle 60, or pi/3.

[Mark44]

The 1, 3, sqrt(10) triangle is NOT a special triangle that you are expected to have memorized. I wonder if there was a typo in your problem, and that maybe it should have been (1 - sqrt(3)i)/i.

[PhysicsMark]

The 1, 3, sqrt(10) triangle is NOT a special triangle that you are expected to have memorized. I wonder if there was a typo in your problem, and that maybe it should have been (1 - sqrt(3)i)/i.

It could have been a typo. I spoke with a few upperclassman who have taken the course and they recommended to leave it implicitly.

I guess tan^-1(3) will have to do. I'm going to speak with the professor before the exam. Thanks for confirming the memorization issue.