What is (sqrt(x)-i)^2 ?

The solution to (sqrt(x)-i)^2 is ((sqrt(x))^2-1)-2sqrt(x)i

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simplify (sqrt(x)-i)^2

simplify

(x - i)^{2}

((x)^{2} - 1) - 2 x i

Solution steps

(x - i)^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

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

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

Apply imaginary number rule:

i^{2} = - 1

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

Rewrite in standard complex form:

((x)^{2} - 1) - 2 x i

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

\frac{9 ( - 189 π + 1620 )}{10}

(sin (y) - y sin (x)) d x + (cos (x) + x cos (y) - y) d y

\frac{10 x + 0.5}{( x ^{2} - 1.2 x + 0.2 ) ( x - 1 )}

\frac{2 ( 2 x - 1 )}{3 ( x ^{2} - x ) ^{\frac{1}{3}}}

\frac{x ^{3} + x ^{2} + 1}{x ( x - 1 ) ( x ^{2} + x + 1 ) ( x ^{2} + 1 ) ^{3}}

What is (sqrt(x)-i)^2 ?
The solution to (sqrt(x)-i)^2 is ((sqrt(x))^2-1)-2sqrt(x)i