What is the answer to 3+4i=(x+yi)(1+i) ?

The answer to 3+4i=(x+yi)(1+i) is x= 7/2 ,y= 1/2

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3+4i=(x+yi)(1+i)

3 + 4 i = (x + y i) (1 + i)

x = \frac{7}{2}, y = \frac{1}{2}

Solution steps

3 + 4 i = (x + y i) (1 + i)

Expand

(x + y i) (1 + i) : (x - y) + i (x + y)

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

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

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

[3 = x - y 4 = x + y] : x = \frac{7}{2}, y = \frac{1}{2}

x = \frac{7}{2}, y = \frac{1}{2}

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

(1 + i) x + (y + 5) i = 3 (1 - y)

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

(x + i y)^{2} = i

(2 + 3 i) x - (1 + i) y = 3 + 4 i

What is the answer to 3+4i=(x+yi)(1+i) ?
The answer to 3+4i=(x+yi)(1+i) is x= 7/2 ,y= 1/2