Question 1077346
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Find the Modulus and argument of the following complex numbers, and write them in trigonometric form: 


<pre>
A) {{{5-8i}}}         The modulus is {{{sqrt(5^2 + (-8)^2)}}} = {{{sqrt(89)}}}.
                 The argument is {{{arctan((-8)/5)}}}.


B) {{{-1- i}}}         The modulus is {{{sqrt((-1)^2 + (-1)^2)}}} = {{{sqrt(2)}}}.
                 The argument is {{{pi + arctan(1)}}} = {{{5pi/4}}}.


C) {{{-5+12i }}}       The modulus is {{{sqrt((-5)^2 + 12^2)}}} = {{{sqrt(169)}}} = 13.
                 The argument is {{{pi - arctan(12/5)}}}.


D) {{{1+ sqrt(3)i}}}         The modulus is {{{sqrt(1^2 + sqrt(3)^2)}}} = {{{sqrt(1+3)}}} = 2.
                 The argument is {{{arctan(sqrt(3))}}} = {{{pi/3}}}.
</pre>


On complex numbers, modulus and arguments, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Complex-numbers-and-arithmetical-operations.lesson>Complex numbers and arithmetic 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, &nbsp;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 under the topic "<U>Complex numbers</U>".



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Notice that you incorrectly wrote your complex number in D).
I fixed your error in my response.