What is the answer to 7x+xi-3yi=3y+9 ?

The answer to 7x+xi-3yi=3y+9 is x= 3/2 ,y= 1/2

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7x+xi-3yi=3y+9

7 x + x i - 3 y i = 3 y + 9

x = \frac{3}{2}, y = \frac{1}{2}

Solution steps

7 x + x i - 3 y i = 3 y + 9

Rewrite

7 x + x i - 3 y i

in standard complex form:

7 x + (x - 3 y) i

7 x + (x - 3 y) i = 3 y + 9

Rewrite

3 y + 9

in standard complex form:

(3 y + 9) + 0 i

7 x + (x - 3 y) i = (3 y + 9) + 0 i

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

[7 x = 3 y + 9 x - 3 y = 0]

[7 x = 3 y + 9 x - 3 y = 0] : x = \frac{3}{2}, y = \frac{1}{2}

x = \frac{3}{2}, y = \frac{1}{2}

(x + y i) (2 - 4 i) = 14 - 18 i

3 z^{2} - 2 + z - 3 i z^{2} + 2 i + z i = 0

∣ z + 3 ∣ = 1 - i z

2 x + 8 i = 6 - (2 y) i

9 x + (y) i - 5 = - 12 i + 4

What is the answer to 7x+xi-3yi=3y+9 ?
The answer to 7x+xi-3yi=3y+9 is x= 3/2 ,y= 1/2