The expression gives a real number as an outcome when x = 4, and y = -5.
Which values of x and y will make the outcome a real number?
Here, you need to remember that the product between a complex number and its complex conjugate is always a real number.
So we only need to define x and y to be such that the second number is the complex conjugate of the first one.
Remember that for a complex number:
[tex]z = a + b*i[/tex]
The complex conjugate is:
[tex]z^* = a - b*i[/tex]
Then the values of x is 4, and the value of y is -5, then we will get:
[tex](4 + 5i)*(4 - 5i) = 16 + 20i - 20i (5)*(-5)*i^2 = 16 + 25 = 41[/tex]
If you want to learn more about complex numbers:
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