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

The answer to (x+iy)(3-i)=-i is x= 1/10 ,y=-3/10

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

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

x = \frac{1}{10}, y = - \frac{3}{10}

Solution steps

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

Expand

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

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

Rewrite

- i

in standard complex form:

0 - i

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

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

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

[3 x + y = 0 - x + 3 y = - 1] : x = \frac{1}{10}, y = - \frac{3}{10}

x = \frac{1}{10}, y = - \frac{3}{10}

(x + 4 i) (x - 4 i) = 0

z = \frac{c - 2 i}{2 - i}

\frac{z + 2}{z - 2} = 3 + i^{27}

∣ z ∣^{2} + 1 + 12 i = 6 z

(x + y i)^{2} = - 7 + 24 i

What is the answer to (x+iy)(3-i)=-i ?
The answer to (x+iy)(3-i)=-i is x= 1/10 ,y=-3/10