What is the answer to (x+iy)(3+i)=5 ?

The answer to (x+iy)(3+i)=5 is x= 3/2 ,y=-1/2

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(x+iy)(3+i)=5

(x + i y) (3 + i) = 5

x = \frac{3}{2}, y = - \frac{1}{2}

Solution steps

(x + i y) (3 + i) = 5

Expand

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

(3 x - y) + i (x + 3 y) = 5

Rewrite

5

in standard complex form:

5 + 0 i

(3 x - y) + i (x + 3 y) = 5 + 0 i

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

[3 x - y = 5 x + 3 y = 0]

[3 x - y = 5 x + 3 y = 0] : x = \frac{3}{2}, y = - \frac{1}{2}

x = \frac{3}{2}, y = - \frac{1}{2}

(1 + i) (x + 2 y) - (3 - 2 i) (x - y) = 8 + 3 i

x + y i = 2

(x + y i) (1 + 2 i) = - 1 + 8 i

\frac{2 - i}{z - 1} = 1 + 2 i

5 x + 6 i = - 20 + 2

What is the answer to (x+iy)(3+i)=5 ?
The answer to (x+iy)(3+i)=5 is x= 3/2 ,y=-1/2