What is the answer to x(1+3i)+y(2-i)-5+i^3=0 ?

The answer to x(1+3i)+y(2-i)-5+i^3=0 is x=1,y=2

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x(1+3i)+y(2-i)-5+i^3=0

x (1 + 3 i) + y (2 - i) - 5 + i^{3} = 0

x = 1, y = 2

Solution steps

x (1 + 3 i) + y (2 - i) - 5 + i^{3} = 0

Expand

x (1 + 3 i) + y (2 - i) - 5 + i^{3} : (x + 2 y - 5) + i (- 1 - y + 3 x)

(x + 2 y - 5) + i (- 1 - y + 3 x) = 0

Rewrite

0

in standard complex form:

0 + 0 i

(x + 2 y - 5) + i (- 1 - y + 3 x) = 0 + 0 i

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

[x + 2 y - 5 = 0 - 1 - y + 3 x = 0]

[x + 2 y - 5 = 0 - 1 - y + 3 x = 0] : x = 1, y = 2

x = 1, y = 2

z_{1} + i z_{2} = 1

x^{2} = - 2 - 23 i

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

z^{2} + 2 i z - 1 = 0

(a + i)^{2} = 8 - 6 i

What is the answer to x(1+3i)+y(2-i)-5+i^3=0 ?
The answer to x(1+3i)+y(2-i)-5+i^3=0 is x=1,y=2