What is the answer to 7x+(x-3y)i=3y+9i ?

The answer to 7x+(x-3y)i=3y+9i is x=-3/2 ,y=-7/2

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

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

x = - \frac{3}{2}, y = - \frac{7}{2}

Solution steps

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

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

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

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

x = - \frac{3}{2}, y = - \frac{7}{2}

\frac{1 + ai}{6 + bi} = 2 + 5 i

3 (5 + 3 bi) + 2 i = 2 a - 7 i

\frac{1 + ( a + bi )}{1 - ( a + bi )} = 2 i

x^{2} + i x - 1 = 0

(x + i y)^{2} = 3 - 4 i

What is the answer to 7x+(x-3y)i=3y+9i ?
The answer to 7x+(x-3y)i=3y+9i is x=-3/2 ,y=-7/2