What is the answer to x+3yi=4-5i ?

The answer to x+3yi=4-5i is x=4,y=-5/3

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x+3yi=4-5i

x + 3 y i = 4 - 5 i

x = 4, y = - \frac{5}{3}

Solution steps

x + 3 y i = 4 - 5 i

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

[x = 4 3 y = - 5]

[x = 4 3 y = - 5] : x = 4, y = - \frac{5}{3}

x = 4, y = - \frac{5}{3}

(x - y) + 3 i = - 6 + y i

(x + i y) (6 - 3 i) = 5 + 6 i

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

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

CM = C (1 + t i)