What is 10(ix+5)(1-ix)(10-ix)(50-ix) ?

The solution to 10(ix+5)(1-ix)(10-ix)(50-ix) is (-10x^4+2550x^2+25000)+(-560x^3-23000x)i

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simplify 10(ix+5)(1-ix)(10-ix)(50-ix)

simplify

10 (i x + 5) (1 - i x) (10 - i x) (50 - i x)

(- 10 x^{4} + 2550 x^{2} + 25000) + (- 560 x^{3} - 23000 x) i

Solution steps

10 (i x + 5) (1 - i x) (10 - i x) (50 - i x)

Rewrite

i x + 5

in standard complex form:

5 + x i

Rewrite

1 - i x

in standard complex form:

1 - x i

Rewrite

10 - i x

in standard complex form:

10 - x i

Rewrite

50 - i x

in standard complex form:

50 - x i

= 10 (5 + x i) (1 - x i) (10 - x i) (50 - x i)

Apply complex arithmetic rule:

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

= 10 ((5 \cdot 1 - x (- x)) + (5 (- x) + x \cdot 1) i) (10 - x i) (50 - x i)

Apply complex arithmetic rule:

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

= 10 (((5 \cdot 1 - x (- x)) \cdot 10 - (5 (- x) + x \cdot 1) (- x)) + ((5 \cdot 1 - x (- x)) (- x) + (5 (- x) + x \cdot 1) \cdot 10) i) (50 - x i)

Apply complex arithmetic rule:

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

= 10 ((((5 \cdot 1 - x (- x)) \cdot 10 - (5 (- x) + x \cdot 1) (- x)) \cdot 50 - ((5 \cdot 1 - x (- x)) (- x) + (5 (- x) + x \cdot 1) \cdot 10) (- x)) + (((5 \cdot 1 - x (- x)) \cdot 10 - (5 (- x) + x \cdot 1) (- x)) (- x) + ((5 \cdot 1 - x (- x)) (- x) + (5 (- x) + x \cdot 1) \cdot 10) \cdot 50) i)

Simplify

(((5 \cdot 1 - x (- x)) \cdot 10 - (5 (- x) + x \cdot 1) (- x)) \cdot 50 - ((5 \cdot 1 - x (- x)) (- x) + (5 (- x) + x \cdot 1) \cdot 10) (- x)) + (((5 \cdot 1 - x (- x)) \cdot 10 - (5 (- x) + x \cdot 1) (- x)) (- x) + ((5 \cdot 1 - x (- x)) (- x) + (5 (- x) + x \cdot 1) \cdot 10) \cdot 50) i : (- x^{4} + 255 x^{2} + 2500) + (- 56 x^{3} - 2300 x) i

= 10 ((- x^{4} + 255 x^{2} + 2500) + (- 56 x^{3} - 2300 x) i)

Expand

10 ((- x^{4} + 255 x^{2} + 2500) + (- 56 x^{3} - 2300 x) i) : - 10 x^{4} + 2550 x^{2} + 25000 - 560 x^{3} i - 23000 x i

= - 10 x^{4} + 2550 x^{2} + 25000 - 560 x^{3} i - 23000 x i

Rewrite in standard complex form:

(- 10 x^{4} + 2550 x^{2} + 25000) + (- 560 x^{3} - 23000 x) i

= (- 10 x^{4} + 2550 x^{2} + 25000) + (- 560 x^{3} - 23000 x) i

\frac{k ( 9 k + 5 )}{2}

(2 - x^{2}) (2 - x^{2})

\frac{( x ^{2} )}{( I n ( 4 - x ) )}

3 x^{2} (4 cos (x) + x sin (x))

(e^{\frac{x}{2}} - e^{- \frac{x}{2}})^{2}

What is 10(ix+5)(1-ix)(10-ix)(50-ix) ?
The solution to 10(ix+5)(1-ix)(10-ix)(50-ix) is (-10x^4+2550x^2+25000)+(-560x^3-23000x)i