What is is*(is+1)*(is+3)*(is+5) ?

The solution to is*(is+1)*(is+3)*(is+5) is (s^4-23s^2)+(15s-9s^3)i

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simplify is(is+1)(is+3)*(is+5)

simplify

i s \cdot (i s + 1) \cdot (i s + 3) \cdot (i s + 5)

(s^{4} - 23 s^{2}) + (15 s - 9 s^{3}) i

Solution steps

i s (i s + 1) (i s + 3) (i s + 5)

Rewrite

i s + 1

in standard complex form:

1 + s i

Rewrite

i s + 3

in standard complex form:

3 + s i

Rewrite

i s + 5

in standard complex form:

5 + s i

= i s (1 + s i) (3 + s i) (5 + s i)

Apply complex arithmetic rule:

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

= i s ((1 \cdot 3 - ss) + (1 \cdot s + s \cdot 3) i) (5 + s i)

Apply complex arithmetic rule:

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

= i s (((1 \cdot 3 - ss) \cdot 5 - (1 \cdot s + s \cdot 3) s) + ((1 \cdot 3 - ss) s + (1 \cdot s + s \cdot 3) \cdot 5) i)

Simplify

((1 \cdot 3 - ss) \cdot 5 - (1 \cdot s + s \cdot 3) s) + ((1 \cdot 3 - ss) s + (1 \cdot s + s \cdot 3) \cdot 5) i : (15 - 9 s^{2}) + (- s^{3} + 23 s) i

= i s ((15 - 9 s^{2}) + (- s^{3} + 23 s) i)

Expand

i s ((15 - 9 s^{2}) + (- s^{3} + 23 s) i) : 15 s i - 9 s^{3} i + s^{4} - 23 s^{2}

= 15 s i - 9 s^{3} i + s^{4} - 23 s^{2}

Rewrite in standard complex form:

(s^{4} - 23 s^{2}) + (15 s - 9 s^{3}) i

= (s^{4} - 23 s^{2}) + (15 s - 9 s^{3}) i

2 (3 + 11)

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

y (w (y, z, x) z^{^{'}} + w (y, z, x) z) + x y

(x - \frac{1}{5}) (x - \frac{2}{5})

What is is*(is+1)*(is+3)*(is+5) ?
The solution to is*(is+1)*(is+3)*(is+5) is (s^4-23s^2)+(15s-9s^3)i