What is the answer to solvefor x,z=(1-xi)/(1+xi) ?

The answer to solvefor x,z=(1-xi)/(1+xi) is x=-(1-z)/(1+z)i

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solvefor x,z=(1-xi)/(1+xi)

solve for

x, z = \frac{1 - x i}{1 + x i}

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

Solution steps

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

Substitute

x = a + bi

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

Multiply both sides by

1 + (a + bi) i

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

Expand

z - z b + i z a = (1 + b) - ia

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

[z - z b = 1 + b z a = - a]

[z - z b = 1 + b z a = - a] : a = 0, b = - \frac{1 - z}{1 + z}, z \neq = - 1

Substitute back

x = a + bi

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

2 x^{2} + i x - 10 = 0

15 + 8 i = a + bi

x^{2} + x (1 + i) + 1 = 0

(3 a + 2 i) - (5 - 2 bi) = 2 - 6 i

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

What is the answer to solvefor x,z=(1-xi)/(1+xi) ?
The answer to solvefor x,z=(1-xi)/(1+xi) is x=-(1-z)/(1+z)i