What is x(x-2)(x-2-i)(x+3+i) ?

The solution to x(x-2)(x-2-i)(x+3+i) is x(x-2)(x^2+x-5)-x(x-2)*5i

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simplify x(x-2)(x-2-i)(x+3+i)

simplify

x (x - 2) (x - 2 - i) (x + 3 + i)

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

Solution steps

x (x - 2) (x - 2 - i) (x + 3 + i)

Rewrite

x - 2 - i

in standard complex form:

(x - 2) - i

= x (x - 2) ((x - 2) - i) (x + 3 + i)

Apply complex arithmetic rule:

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

= x (x - 2) (((x - 2) (x + 3) - (- 1) \cdot 1) + ((x - 2) \cdot 1 - 1 \cdot (x + 3)) i)

Simplify

((x - 2) (x + 3) - (- 1) \cdot 1) + ((x - 2) \cdot 1 - 1 \cdot (x + 3)) i : (x^{2} + x - 5) - 5 i

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

Distribute parentheses

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

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

lo g_{10} (a) ((x^{2} + 1) 4 x)

K \cdot (1 + \frac{1}{T})

\frac{d}{d t} ((s) (7 t^{3} - 3 t^{7}))

(1 - 3 i)^{11}

What is x(x-2)(x-2-i)(x+3+i) ?
The solution to x(x-2)(x-2-i)(x+3+i) is x(x-2)(x^2+x-5)-x(x-2)*5i