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

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

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3+yi=x-7i

3 + y i = x - 7 i

x = 3, y = - 7

Solution steps

3 + y i = x - 7 i

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

[3 = x y = - 7]

[3 = x y = - 7] : x = 3, y = - 7

x = 3, y = - 7

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

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

∣ z ∣ - z = 1 + 2 i

(x + i y) (2 + 3 i) = 1 - 5 i

∣ z - i ∣ = 2