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

The answer to (1-i)x+3y=2-1 is x=0,y= 1/3

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

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

x = 0, y = \frac{1}{3}

Solution steps

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

Rewrite

(1 - i) x + 3 y

in standard complex form:

(x + 3 y) - x i

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

Rewrite

2 - 1

in standard complex form:

(2 - 1) + 0 i

(x + 3 y) - x i = (2 - 1) + 0 i

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

[x + 3 y = 2 - 1 - x = 0]

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

x = 0, y = \frac{1}{3}

a, a + bi = a + c i

(2 x + 12 y) + (x + y) i = 6 - 2 i

(a - 2 bi) - (b - ai) = 2 + i

a + bi = i

(a + 2 i) (b - i) = 3 + i