Question 1194520
.
<pre>

(c)  Z1 * Z2 = (2-2i)*(-3+i) = -6 + 6i + 2i -2i^2 = -6 + 8i -2*(-1) =

             = -6 + 8i + 2 = -4 + 8i.



(e)  The angle (the argument) for Z1 is  {{{-pi/4}}} = -45°.

     The angle (the argument) for Z2 is  {{{pi/2}}} =   90°.


     THEREFORE, the angle between Z1 and Z2 is  {{{pi/2}}} - {{{(-pi/4)}}} = {{{3pi/4}}}.

                Or, in degrees,  the angle between Z1 and Z2 is 90° - (-45°) = 135°.



         This answer is for minimal angle measure.  
     
         The other possible angle "between" these complex numbers is 360° - 135° = 225°,

         but normally, the minimal of the two angles is considered as the answer.
</pre>

---------------


On complex numbers, &nbsp;see introductory lessons

&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>

in this site.


Also, &nbsp;you have this free of charge online textbook on &nbsp;ALGEBRA-II &nbsp;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 &nbsp;"<U>Complex numbers</U>".



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.