What is the answer to ((4+xi))/(2+i)=y+2i ?

The answer to ((4+xi))/(2+i)=y+2i is x=7,y=3

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((4+xi))/(2+i)=y+2i

\frac{( 4 + x i )}{2 + i} = y + 2 i

x = 7, y = 3

Solution steps

\frac{( 4 + x i )}{2 + i} = y + 2 i

Multiply both sides by

2 + i

\frac{4 + x i}{2 + i} (2 + i) = y (2 + i) + 2 i (2 + i)

Expand

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

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

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

[4 = 2 y - 2 x = 4 + y] : x = 7, y = 3

x = 7, y = 3

2 x + 7 + (3 - y) i = - 4 + 6 i

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

z^{2} - (2 + 2 i) z + (1 + 2 i) = 0

(x + y \cdot i)^{2} = i

(x + y i) = - 8

What is the answer to ((4+xi))/(2+i)=y+2i ?
The answer to ((4+xi))/(2+i)=y+2i is x=7,y=3