Question 1095676
.
solve the following equation for real numbers x and y.
(a).(3+4i)^2-2(x-iy)=x+iy
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<pre>
(3+4i)^2-2(x-iy)=x+iy            <==== is equivalent ====>

(3+4i)^2 = (x + iy) + 2*(x-iy)   <==== is equivalent ====>

9 + 24i - 16 = 3x -iy            <==== is equivalent ====>

-7 + 24i = 3x - iy               <==== is equivalent ====>


to this system of two equations in two unknowns:

3x = -7
-y = 24.


SOLUTION:  x = -7/3, y = 24.
</pre>

All you need to know to solve the problem is <U>THIS</U>:


<pre>
    two complex numbers are equal if and only if their real parts are equal AND their imaginary parts are equal.
</pre>


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On complex numbers, see these 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>


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/Solved-problems-on-arithmetic-operations-on-complex-numbers.lesson>Solved problems on arithmetic operations on complex numbers</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 &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.