What is ix(ix+3)(ix+6) ?

The solution to ix(ix+3)(ix+6) is -9x^2+(18x-x^3)i

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simplify ix(ix+3)(ix+6)

simplify

i x (i x + 3) (i x + 6)

- 9 x^{2} + (18 x - x^{3}) i

Solution steps

i x (i x + 3) (i x + 6)

Rewrite

i x + 3

in standard complex form:

3 + x i

Rewrite

i x + 6

in standard complex form:

6 + x i

= i x (3 + x i) (6 + x i)

Apply complex arithmetic rule:

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

= i x ((3 \cdot 6 - xx) + (3 x + x \cdot 6) i)

Simplify

(3 \cdot 6 - xx) + (3 x + x \cdot 6) i : (18 - x^{2}) + 9 x i

= i x ((18 - x^{2}) + 9 x i)

Expand

i x ((18 - x^{2}) + 9 x i) : 18 x i - x^{3} i - 9 x^{2}

= 18 x i - x^{3} i - 9 x^{2}

Rewrite in standard complex form:

- 9 x^{2} + (18 x - x^{3}) i

= - 9 x^{2} + (18 x - x^{3}) i

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

(x e^{a x}) (e^{b x} + b e^{b x} x)

\frac{t ( t - 2 )}{( 1 + t ) ( 1 - t )}

\frac{5 x}{( 2 - x ) ( x + 4 )}

A (- 8, 3) y B (- 2, - 5)