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

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

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

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

x = 2, y = - 1

Solution steps

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

Rewrite

(x + y) i + 3 y

in standard complex form:

3 y + (x + y) i

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

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

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

[3 y = - 3 x + y = 1] : x = 2, y = - 1

x = 2, y = - 1

a - bi - 1 = \frac{15 + 8 i}{4 ( a + bi )}

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

\frac{2 i z}{1 + i} = \frac{i}{- z}

x + i y = 1

2 x^{2} + 2 x i - y^{2} - y i - 2 i = 2