simplify (x-5i)^2

Solution

simplify

(x - 5 i)^{2}

(x^{2} - 25) - 10 x i

Solution steps

(x - 5 i)^{2}

Apply Perfect Square Formula:

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

(x - 5 i)^{2} = x^{2} - 2 x \cdot 5 i + (5 i)^{2}

= x^{2} - 2 x \cdot 5 i + (5 i)^{2}

- 2 x \cdot 5 i = - 10 x i

(5 i)^{2} = - 25

= x^{2} - 10 x i - 25

Rewrite in standard complex form:

(x^{2} - 25) - 10 x i

= (x^{2} - 25) - 10 x i

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

\frac{( tan ( x ) + sin ( x ) ) cos ( x )}{csc ( x ) + cot ( x )}

\frac{n !}{n ( n - 1 )}

\frac{d}{d t} ((x (t, r)) (r (t - sin (t))))

\frac{d ^{2}}{d x ^{2}} ((y) (cos (π x y) - \frac{1}{x} + \frac{2}{y ^{3}}))