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


You probably know that cos(pi/3) = {{{1/2}}} and sin(pi/3) = {{{sqrt(3)/2}}}.


Substitute it in the formula for z. You will get

z = {{{4*((1/2) + i*(sqrt(3)/2))}}} = {{{2 + i*2*sqrt(3)}}}.

That's all with this case.


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

Use cos(5pi/6) = {{{sqrt(3)/2}}} and sin(5pi/6) = {{{-1/2}}}.
</pre>

There is a bunch of my lessons on complex numbers

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Complex-numbers-and-arithmetical-operations.lesson>Complex numbers and arithmetical operations on them</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Complex-plane.lesson>Complex plane</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Addition-and-subtraction-of-complex-numbers-in-complex-plane.lesson>Addition and subtraction of complex numbers in complex plane</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Multiplication-and-division-of-complex-numbers-in-complex-plane-.lesson>Multiplication and division of complex numbers in complex plane</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Raising-a-complex-number-to-an-integer-power.lesson>Raising a complex number to an integer power</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/How-to-take-a-root-of-a-complex-number.lesson>How to take a root of a complex number</A>

in this site.


Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook.