If \(x+iy=\begin{vmatrix}6i & -3i & 1 \\\ 4 & 3i & -1 \\\ 20 & 3 & i \end{vmatrix}\) then what is x - iy equal to?

Concept:

i2 = - 1

Calculations:

Given, \(x+iy=\begin{vmatrix}6i & -3i & 1 \\\ 4 & 3i & -1 \\\ 20 & 3 & i \end{vmatrix}\)

⇒ x + iy = 6i (3i² + 3) + 3i (4i + 20) + 1(12 - 60i)

⇒ x + iy = 6i (3i2 + 3) + 12i2 + 60i + 12 - 60i

We know that i2 = - 1

⇒ x + iy = 6i [3(-1)+3] +12(-1) + 60i + 12 - 60i

⇒ x + iy = 0 

⇒ x + iy = 0 + i 0

⇒ x = 0 and y = 0

Consider,  x - iy

Put the value of x and y in above expression, we get

⇒ x - iy = 0 - i0

⇒ x - iy = 0 

Hint

To find the value of x - iy, find the value of x and y.

To find the value of x and y, solve the given determinant and compare the real and imaginary part.