Find the value of x and y if (x+2y)+i(2x-3y) is conjute of 5+4i.
the conjugate is 5-4i
So, you need
x+2y = 5
2x-3y = -4
Now just crank it out.
Thank you very much
To find the values of x and y, we need to equate the real and imaginary parts of the given complex expression to the real and imaginary parts of the conjugate of 5+4i.
Let's start with the given complex expression:
(x + 2y) + i(2x - 3y)
To find the conjugate of a complex number, we change the sign of the imaginary part. The conjugate of 5+4i is 5-4i. So, we can equate the real and imaginary parts separately.
Equating the real parts:
x + 2y = 5
Equating the imaginary parts:
2x - 3y = -4
Now we have a system of two equations with two variables. We can use any method (substitution, elimination, matrices, etc.) to solve for x and y.
Let's solve it using the substitution method:
From the first equation, we can isolate x:
x = 5 - 2y
Now, substitute this value of x into the second equation:
2(5 - 2y) - 3y = -4
10 - 4y - 3y = -4
10 - 7y = -4
-7y = -14
y = -14 / -7
y = 2
Now substitute the value of y back into the first equation to find x:
x + 2(2) = 5
x + 4 = 5
x = 5 - 4
x = 1
Therefore, the values of x and y are:
x = 1
y = 2