What is the answer to (7+2i)(x-iy)=5i(x+iy)-14i ?

The answer to (7+2i)(x-iy)=5i(x+iy)-14i is x=-7/2 ,y= 7/2

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(7+2i)(x-iy)=5i(x+iy)-14i

(7 + 2 i) (x - i y) = 5 i (x + i y) - 14 i

x = - \frac{7}{2}, y = \frac{7}{2}

Solution steps

(7 + 2 i) (x - i y) = 5 i (x + i y) - 14 i

Expand

(7 x + 2 y) + i (2 x - 7 y) = - 5 y + i (- 14 + 5 x)

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[7 x + 2 y = - 5 y 2 x - 7 y = - 14 + 5 x]

[7 x + 2 y = - 5 y 2 x - 7 y = - 14 + 5 x] : x = - \frac{7}{2}, y = \frac{7}{2}

x = - \frac{7}{2}, y = \frac{7}{2}

λ = (λ + i) (λ + 5 - i (λ - 7))

3 x + (2 x - y) i = 6 - 3 i

(a + bi)^{2} = - 4

m^{2} = i

(x - 3) + (8 - y) i = - 3 + 4 i

What is the answer to (7+2i)(x-iy)=5i(x+iy)-14i ?
The answer to (7+2i)(x-iy)=5i(x+iy)-14i is x=-7/2 ,y= 7/2