What is the answer to (x+iy)(2+1)=3-i ?

The answer to (x+iy)(2+1)=3-i is x=1,y=-1/3

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

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

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

Solution steps

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

Rewrite

(x + i y) (2 + 1)

in standard complex form:

3 x + 3 y i

3 x + 3 y i = 3 - i

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

[3 x = 3 3 y = - 1]

[3 x = 3 3 y = - 1] : x = 1, y = - \frac{1}{3}

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

3 x + 8 i = 12 + 12

(x + y) + (x - y) \cdot i = 5 + 5 \cdot i

5 x + 6 i = - 8 + 6

- 3 - 4 i = (a + bi)^{2}

5 x + (7 x - 2 y) i = 2 + 8 i

What is the answer to (x+iy)(2+1)=3-i ?
The answer to (x+iy)(2+1)=3-i is x=1,y=-1/3