Which values of x and y would make the following expression represent a real number?(4 + 5i)(x + yi)
To determine the values of x and y that would make the expression (4 + 5i)(x + yi) represent a real number, we need to consider the properties of complex numbers
To determine the values of x and y that would make the expression (4 + 5i)(x + yi) represent a real number, we need to consider the properties of complex numbers.
First, let’s simplify the expression by performing the multiplication:
(4 + 5i)(x + yi) = 4x + 4yi + 5ix + 5i^2
Remember that i^2 is equal to -1, so the expression becomes:
4x + 4yi + 5ix + 5(-1)
4x + 4yi + 5ix – 5
Now, in order to represent a real number, the imaginary part of the expression (4yi + 5ix) should be equal to zero. This means that the coefficient of y (4y) and the coefficient of i multiplied by x (5x) should both equal zero.
Therefore, we get two equations:
4y = 0 — (1)
5x = 0 — (2)
From equation (1), we can see that y must be equal to zero in order for the expression to be real.
From equation (2), x must also be equal to zero for the expression to be real.
Thus, the values of x and y that would make the expression (4 + 5i)(x + yi) represent a real number are x = 0 and y = 0.
In conclusion, when both x and y are equal to zero, the expression (4 + 5i)(x + yi) represents a real number.
More Answers:
[next_post_link]