SOLUTION: Given that z_1 = 4[cos (pi/3) + i sin (pi/3)] and z_2 = 2[cos (5pi/6) + i sin (5pi/6)] are complex numbers, find z_2 - z_1. I have to write them in rectangular form, and I don't

Question 1053020: Given that z_1 =
4[cos (pi/3) + i sin (pi/3)] and z_2 = 2[cos (5pi/6) + i sin (5pi/6)]
are complex numbers, find z_2 - z_1. I have to write them in rectangular form, and I don't know how.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
Given that z_1 =
4[cos (pi/3) + i sin (pi/3)] and z_2 = 2[cos (5pi/6) + i sin (5pi/6)]
are complex numbers, find z_2 - z_1. I have to write them in rectangular form, and I don't know how.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

z = 4(cos (pi/3) + i sin (pi/3)).


You probably know that cos(pi/3) =  and sin(pi/3) = .


Substitute it in the formula for z. You will get

z =  = .

That's all with this case.


For the other z do the same (or similar).

Use cos(5pi/6) =  and sin(5pi/6) = .

There is a bunch of my lessons on complex numbers
    - Complex numbers and arithmetical operations on them
    - Complex plane
    - Addition and subtraction of complex numbers in complex plane
    - Multiplication and division of complex numbers in complex plane
    - Raising a complex number to an integer power
    - How to take a root of a complex number
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook.

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