What is (iw+0.5)*(iw+1)*(iw+2) ?

The solution to (iw+0.5)*(iw+1)*(iw+2) is (1-3.5w^2)+(-w^3+3.5w)i

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simplify (iw+0.5)(iw+1)(iw+2)

simplify

(i w + 0.5) \cdot (i w + 1) \cdot (i w + 2)

(1 - 3.5 w^{2}) + (- w^{3} + 3.5 w) i

Solution steps

(i w + 0.5) (i w + 1) (i w + 2)

Rewrite

i w + 0.5

in standard complex form:

0.5 + w i

Rewrite

i w + 1

in standard complex form:

1 + w i

Rewrite

i w + 2

in standard complex form:

2 + w i

= (0.5 + w i) (1 + w i) (2 + w i)

Apply complex arithmetic rule:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= ((0.5 \cdot 1 - ww) + (0.5 w + w \cdot 1) i) (2 + w i)

Apply complex arithmetic rule:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= ((0.5 \cdot 1 - ww) \cdot 2 - (0.5 w + w \cdot 1) w) + ((0.5 \cdot 1 - ww) w + (0.5 w + w \cdot 1) \cdot 2) i

Simplify

((0.5 \cdot 1 - ww) \cdot 2 - (0.5 w + w \cdot 1) w) + ((0.5 \cdot 1 - ww) w + (0.5 w + w \cdot 1) \cdot 2) i : (1 - 3.5 w^{2}) + (- w^{3} + 3.5 w) i

= (1 - 3.5 w^{2}) + (- w^{3} + 3.5 w) i

(z + 1 + i)^{2}

\frac{( 8 x - 5 )}{( 4 x - 7 ) ^{2}}

- \frac{16 x ( - x ^{2} + 12 )}{( x ^{2} + 4 ) ^{3}}

\frac{( e ^{3 s} - e ^{4 s} )}{( s - 4 ) ( s + 1 )}

(cos (θ) + sin (θ)) (cos (θ))

What is (iw+0.5)*(iw+1)*(iw+2) ?
The solution to (iw+0.5)*(iw+1)*(iw+2) is (1-3.5w^2)+(-w^3+3.5w)i