What is the answer to 3+x+i=7+yi ?

The answer to 3+x+i=7+yi is x=4,y=1

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3+x+i=7+yi

3 + x + i = 7 + y i

x = 4, y = 1

Solution steps

3 + x + i = 7 + y i

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

[3 + x = 7 1 = y]

[3 + x = 7 1 = y] : x = 4, y = 1

x = 4, y = 1

- 2 x i + 3 x - 5 y - 10 = - 4 y i - 5 x + 8 i

z^{2} = - 2 i

3 + y i = x - 7 i

z^{2} - (1 - 2 i) z + (8 + 2 i) = 0

z - \frac{1}{z} = 5 + 4 i