simplify (iw+1)^2

Solution

simplify

(i w + 1)^{2}

(- w^{2} + 1) + 2 w i

Solution steps

(i w + 1)^{2}

Apply Perfect Square Formula:

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

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

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

(i w)^{2} = - w^{2}

2 i w \cdot 1 = 2 w i

1^{2} = 1

= - w^{2} + 2 w i + 1

Rewrite in standard complex form:

(- w^{2} + 1) + 2 w i

= (- w^{2} + 1) + 2 w i

\frac{x ^{2} + 6 x + 9}{( x - 1 ) ( x - 2 ) ( x + 4 )}

lo g_{3} (2.5)

\frac{( s + 2 ) ( s + 4 )}{s ( s + 1 ) ( s + 5 ) ( s + 10 )}

\frac{2 ( 4 w + 10 )}{3} (= - 3)

2 (5 - 5)