What is the answer to 3x-y=i+2ix-iy ?

The answer to 3x-y=i+2ix-iy is x=1,y=3

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3x-y=i+2ix-iy

3 x - y = i + 2 i x - i y

x = 1, y = 3

Solution steps

3 x - y = i + 2 i x - i y

Rewrite

3 x - y

in standard complex form:

(3 x - y) + 0 i

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

Rewrite

i + 2 i x - i y

in standard complex form:

0 + (1 + 2 x - y) i

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

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

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

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

x = 1, y = 3

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

∣ 2 z + i ∣ = 4

r, i = \frac{v}{r}

5 x + i 5 y = 100, 5 y + i (5 x - 10 y) = 60 + i 80

x^{2} + (4 - 2 i) x + 3 = 0