What is the answer to 25-m^2=(-1)^2+(mi+2i)^2 ?

The answer to 25-m^2=(-1)^2+(mi+2i)^2 is m=-7

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25-m^2=(-1)^2+(mi+2i)^2

25 - m^{2} = (- 1)^{2} + (mi + 2 i)^{2}

m = - 7

Solution steps

25 - m^{2} = (- 1)^{2} + (mi + 2 i)^{2}

Substitute

m = x + y i

25 - (x + y i)^{2} = (- 1)^{2} + ((x + y i) i + 2 i)^{2}

Expand

(25 - x^{2} + y^{2}) - 2 i x y = (- x^{2} - 4 x + y^{2} - 3) + i (- 4 y - 2 x y)

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

[25 - x^{2} + y^{2} = - x^{2} - 4 x + y^{2} - 3 - 2 x y = - 4 y - 2 x y]

[25 - x^{2} + y^{2} = - x^{2} - 4 x + y^{2} - 3 - 2 x y = - 4 y - 2 x y] : (x = - 7, y = 0)

Substitute back

m = x + y i

m = - 7

\frac{z - 5 i}{z + 2} = 4 i

3 x + 2 y i - i x + 5 y = 7 + 5 i

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

z - (\frac{1}{z}) = 1 + 5 i

z^{2} = - (\frac{4 i}{3})

What is the answer to 25-m^2=(-1)^2+(mi+2i)^2 ?
The answer to 25-m^2=(-1)^2+(mi+2i)^2 is m=-7