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

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

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

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

x = \frac{3}{13}, y = - \frac{2}{13}

Solution steps

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

Rewrite

- i

in standard complex form:

0 - i

(2 x + 3 y) + i (2 y - 3 x) = 0 - i

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

[2 x + 3 y = 0 2 y - 3 x = - 1]

[2 x + 3 y = 0 2 y - 3 x = - 1] : x = \frac{3}{13}, y = - \frac{2}{13}

x = \frac{3}{13}, y = - \frac{2}{13}

(x + 6 i) = (3 - i) + (4 - 2 y i)

(3 + 4 i)^{2} - 2 (x - i y) = x + i y

3 x - y - i = 2 i x - i y

x^{2} - 8 i x - 25 = 0

- 4 + (y) i = - 12 x - i + 8

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