What is the answer to 0=(1+λi)/(1-λi) ?

The answer to 0=(1+λi)/(1-λi) is λ=i

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0=(1+λi)/(1-λi)

0 = \frac{1 + λi}{1 - λi}

λ = i

Solution steps

0 = \frac{1 + λi}{1 - λi}

Substitute

λ = x + y i

0 = \frac{1 + ( x + y i ) i}{1 - ( x + y i ) i}

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

0 = 1 + (x + y i) i

Simplify

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

0 = (1 - y) + i x

Rewrite

0

in standard complex form:

0 + 0 i

0 + 0 i = (1 - y) + i x

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

[0 = 1 - y 0 = x]

[0 = 1 - y 0 = x] : x = 0, y = 1

Substitute back

λ = x + y i

λ = i

z^{2} - (1 - 2 i) z + (2 - 16 i) = 0

(8 + 9 i) y - (3 + 6 i) x = 16 - 3 i

(5 - 3 i) y - (6 + 2 i) x = 3 - 41 i

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

a = [aij]