What is the answer to (1+2i)x+(3-5i)y=1-3i ?

The answer to (1+2i)x+(3-5i)y=1-3i is x=-4/11 ,y= 5/11

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(1+2i)x+(3-5i)y=1-3i

(1 + 2 i) x + (3 - 5 i) y = 1 - 3 i

x = - \frac{4}{11}, y = \frac{5}{11}

Solution steps

(1 + 2 i) x + (3 - 5 i) y = 1 - 3 i

Rewrite

(1 + 2 i) x + (3 - 5 i) y

in standard complex form:

(x + 3 y) + (2 x - 5 y) i

(x + 3 y) + (2 x - 5 y) i = 1 - 3 i

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

[x + 3 y = 1 2 x - 5 y = - 3]

[x + 3 y = 1 2 x - 5 y = - 3] : x = - \frac{4}{11}, y = \frac{5}{11}

x = - \frac{4}{11}, y = \frac{5}{11}

r (t) = t^{3} i + t^{2} j

z^{2} = - 2 + 23 i

x^{2} = 1 + i

∣ 2 z - i ∣ = 4

v = i r

What is the answer to (1+2i)x+(3-5i)y=1-3i ?
The answer to (1+2i)x+(3-5i)y=1-3i is x=-4/11 ,y= 5/11