What is the answer to (x+yi)(2-4i)=14-18i ?

The answer to (x+yi)(2-4i)=14-18i is x=5,y=1

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(x+yi)(2-4i)=14-18i

(x + y i) (2 - 4 i) = 14 - 18 i

x = 5, y = 1

Solution steps

(x + y i) (2 - 4 i) = 14 - 18 i

Expand

(x + y i) (2 - 4 i) : (2 x + 4 y) + i (2 y - 4 x)

(2 x + 4 y) + i (2 y - 4 x) = 14 - 18 i

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

[2 x + 4 y = 14 2 y - 4 x = - 18]

[2 x + 4 y = 14 2 y - 4 x = - 18] : x = 5, y = 1

x = 5, y = 1

3 z^{2} - 2 + z - 3 i z^{2} + 2 i + z i = 0

∣ z + 3 ∣ = 1 - i z

2 x + 8 i = 6 - (2 y) i

9 x + (y) i - 5 = - 12 i + 4

i = (a + bi)^{2}

What is the answer to (x+yi)(2-4i)=14-18i ?
The answer to (x+yi)(2-4i)=14-18i is x=5,y=1