What is the answer to (3+3i)(x+yi)=27-3i ?

The answer to (3+3i)(x+yi)=27-3i is x=4,y=-5

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(3+3i)(x+yi)=27-3i

(3 + 3 i) (x + y i) = 27 - 3 i

x = 4, y = - 5

Solution steps

(3 + 3 i) (x + y i) = 27 - 3 i

Expand

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

(3 x - 3 y) + i (3 x + 3 y) = 27 - 3 i

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

[3 x - 3 y = 27 3 x + 3 y = - 3]

[3 x - 3 y = 27 3 x + 3 y = - 3] : x = 4, y = - 5

x = 4, y = - 5

(4 + 2 i) (3 - i) = a + bi

z^{2} + (2 i - 3) z + (5 - i) = 0

a, \frac{1}{a + bi} = c + d i

5 + (x^{2} - 6 x + 9) i = 0

3 z^{2} - (5 - 4 i) z + (2 - 3 i) = 0

What is the answer to (3+3i)(x+yi)=27-3i ?
The answer to (3+3i)(x+yi)=27-3i is x=4,y=-5