What is the answer to (x+yi)(2-3i)=4+i ?

The answer to (x+yi)(2-3i)=4+i is x= 5/13 ,y= 14/13

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(x+yi)(2-3i)=4+i

(x + y i) (2 - 3 i) = 4 + i

x = \frac{5}{13}, y = \frac{14}{13}

Solution steps

(x + y i) (2 - 3 i) = 4 + i

Expand

(x + y i) (2 - 3 i) : (2 x + 3 y) + i (2 y - 3 x)

(2 x + 3 y) + i (2 y - 3 x) = 4 + i

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

[2 x + 3 y = 4 2 y - 3 x = 1]

[2 x + 3 y = 4 2 y - 3 x = 1] : x = \frac{5}{13}, y = \frac{14}{13}

x = \frac{5}{13}, y = \frac{14}{13}

(3 + 2 i) (2 - 3 i) - (1 + 2 i) (2 - i) = m + ni

∣ z - 5 - 6 i ∣ = 4

a (2 - i) + b (3 + i) = 10

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

- 1 - i = x i + y

What is the answer to (x+yi)(2-3i)=4+i ?
The answer to (x+yi)(2-3i)=4+i is x= 5/13 ,y= 14/13