simplify (1+5xi)^2

Solution

simplify

(1 + 5 x i)^{2}

(1 - 25 x^{2}) + 10 x i

Solution steps

(1 + 5 x i)^{2}

Apply Perfect Square Formula:

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

(1 + 5 x i)^{2} = 1^{2} + 2 \cdot 1 \cdot 5 x i + (5 x i)^{2}

= 1^{2} + 2 \cdot 1 \cdot 5 x i + (5 x i)^{2}

1^{2} = 1

2 \cdot 1 \cdot 5 x i = 10 x i

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

= 1 + 10 x i - 25 x^{2}

Rewrite in standard complex form:

(1 - 25 x^{2}) + 10 x i

= (1 - 25 x^{2}) + 10 x i

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

sin (x) (1 + cos (x))

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

tan (x) (1 - cot^{2} (x)) + cot (x) (1 - tan^{2} (x))