What is the answer to |x+yi|=y-ix ?

The answer to |x+yi|=y-ix is No Solution

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|x+yi|=y-ix

∣ x + y i ∣ = y - i x

No Solution

Solution steps

∣ x + y i ∣ = y - i x

Simplify

∣ x + y i ∣ : x^{2} + y^{2}

x^{2} + y^{2} = y - i x

Rewrite

x^{2} + y^{2}

in standard complex form:

x^{2} + y^{2} + 0 i

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

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

[x^{2} + y^{2} = y 0 = - x]

[x^{2} + y^{2} = y 0 = - x] : No Solution

No Solution

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

- y + x i = x - y i

\frac{2 + ai}{4 + bi} = 2 + 5 i

w = \frac{p + 4 i}{1 + i p}

25 x^{2} + 60 x + 37 = 0 a + bia + bi