SOLUTION: solve the following equation for real numbers x and y. (a).(3+4i)^2-2(x-iy)=x+iy

Question 1095676: solve the following equation for real numbers x and y.
(a).(3+4i)^2-2(x-iy)=x+iy
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.
solve the following equation for real numbers x and y.
(a).(3+4i)^2-2(x-iy)=x+iy
~~~~~~~~~~~~~~~~~~~

(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.

All you need to know to solve the problem is THIS:

    two complex numbers are equal if and only if their real parts are equal AND their imaginary parts are equal.

-------------
On complex numbers, see these introductory lessons
    - 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

    - Solved problems on arithmetic operations on complex numbers
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 under the topic "Complex numbers".

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.

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