What is the answer to sqrt(a^2-b^2)-a-bi=1 ?

The answer to sqrt(a^2-b^2)-a-bi=1 is

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sqrt(a^2-b^2)-a-bi=1

a^{2} - b^{2} - a - bi = 1

(a = - \frac{1}{2}, b = 0)

Solution steps

a^{2} - b^{2} - a - bi = 1

Rewrite

1

in standard complex form:

1 + 0 i

a^{2} - b^{2} - a - bi = 1 + 0 i

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

[a^{2} - b^{2} - a = 1 - b = 0]

[a^{2} - b^{2} - a = 1 - b = 0] : (a = - \frac{1}{2}, b = 0)

(a = - \frac{1}{2}, b = 0)

(2 x - 3 y i) (1 - 2 i) = 1 - 4 i

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

(1 + 2 i) (x + y i) - (1 + 2 i) (x - y i) = 16

z^{2} = - 4 i

z^{2} + 2 - 4 i = 0

What is the answer to sqrt(a^2-b^2)-a-bi=1 ?
The answer to sqrt(a^2-b^2)-a-bi=1 is