What is the answer to 8+(3x+y)i=2x-4i ?

The answer to 8+(3x+y)i=2x-4i is x=4,y=-16

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8+(3x+y)i=2x-4i

8 + (3 x + y) i = 2 x - 4 i

x = 4, y = - 16

Solution steps

8 + (3 x + y) i = 2 x - 4 i

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

[8 = 2 x 3 x + y = - 4]

[8 = 2 x 3 x + y = - 4] : x = 4, y = - 16

x = 4, y = - 16

x + y i = \frac{i ^{3}}{2 - i}

3 + 4 i = (x + y i) (1 + i)

(3 - 2 i) (x + i y) = 2 (x - 2 i y) + 2 i - 1

(1 + i) x + (y + 5) i = 3 (1 - y)

(1 - i) x + (1 + i) y = 1 - 3 i

What is the answer to 8+(3x+y)i=2x-4i ?
The answer to 8+(3x+y)i=2x-4i is x=4,y=-16