Rectangular to Polar without Calculator

[Dalmain]

Good Afternoon Everyone, hope you are all well.

I've been asked to convert a complex number from rectangular form to polar form, which I normally don't have an issue with, but they have said no calculators!!

I have drawn the Argand diagram and worked out the modulus as below.



With the angle, I get as far as



Now the textbook shows the answer is



but I don't understand how to convert the square root of 3 to pi over 3 without using a calculator?

As always, any assistance is appreciated.

 

[Dr.Peterson]

Good Afternoon Everyone, hope you are all well.

I've been asked to convert a complex number from rectangular form to polar form, which I normally don't have an issue with, but they have said no calculators!!

I have drawn the Argand diagram and worked out the modulus as below.

View attachment 33260

With the angle, I get as far as

View attachment 33261

Now the textbook shows the answer is

View attachment 33262

but I don't understand how to convert the square root of 3 to pi over 3 without using a calculator?

As always, any assistance is appreciated.

You should have learned the trig functions of special angles, one of which is pi/3. You are expected to recognize that tan(pi/3) = sqrt(3):

Functions of Special Angles (Trig without Tears Part 3)

Learn the functions for certain special angles (multiples of 30 deg or pi/6 and 45 deg or pi/4)

brownmath.com

 

[Dalmain]

Thank you again, Dr. Peterson. This wasn't covered in my module so I will learn it from the link you've attached. I think you are single-handedly going to get me through my diploma! Thank you again