Given,19286)23( iyxi  find the complex numbers x and y if x is thecomplex conjugate of y

To find the complex numbers x and y, we are given the equation 19286)23( iyxi .

Step 1: We know that x is the complex conjugate of y. This means that the real parts of x and y are the same, but the imaginary parts have opposite signs.

Step 2: Let's assume that x = a + bi and y = a - bi, where a and b are real numbers.

Step 3: Substituting these values into the given equation, we have 19286)23( i(a - bi)(a + bi) .

Step 4: Simplifying the equation, we get 19286)23( i(a^2 - (bi)^2) .

Step 5: Expanding the equation, we have 19286)23( i(a^2 - b^2i^2) .

Step 6: Since i^2 = -1, we can simplify further to 19286)23( i(a^2 + b^2) .

Step 7: Equating the real and imaginary parts of the equation separately, we have:

Real part: 19286)23( (a^2 + b^2) = 19

Imaginary part: 19286)23( (a^2 + b^2) = 286

Step 8: Solving these two equations simultaneously, we can find the values of a and b.

Step 9: Once we have the values of a and b, we can substitute them back into the expressions for x and y to find the complex numbers x and y.