What is the answer to (x+iy)(6-3i)=5+6i ?

The answer to (x+iy)(6-3i)=5+6i is x= 4/15 ,y= 17/15

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

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

x = \frac{4}{15}, y = \frac{17}{15}

Solution steps

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

Expand

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

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

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

[6 x + 3 y = 5 - 3 x + 6 y = 6]

[6 x + 3 y = 5 - 3 x + 6 y = 6] : x = \frac{4}{15}, y = \frac{17}{15}

x = \frac{4}{15}, y = \frac{17}{15}

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

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

CM = C (1 + t i)

(3 + 2 i)^{2} y = (x + 3 i)^{2}

(4 x - 18.6 - 4 y) = (6 y) i + (4 x - 2) j

What is the answer to (x+iy)(6-3i)=5+6i ?
The answer to (x+iy)(6-3i)=5+6i is x= 4/15 ,y= 17/15