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

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

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

simplify

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

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

Solution steps

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

Rewrite

1 - i w

in standard complex form:

1 - w i

Rewrite

5 + i w

in standard complex form:

5 + w i

Rewrite

10 - i w

in standard complex form:

10 - w i

Rewrite

50 - i w

in standard complex form:

50 - w i

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

Apply complex arithmetic rule:

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

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

Apply complex arithmetic rule:

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

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

Apply complex arithmetic rule:

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

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

Simplify

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

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

Expand

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

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

Rewrite in standard complex form:

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

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

\frac{3 x - 12}{( x + 5 ) ( x - 10 )}

(4 x + \frac{4}{3}) (5 x - 1)

\frac{1}{( s - 3 ) ^{3}}

(e^{3 x + 1}) (2 x + 1)^{3}

(1, 2, 1, 1) y (2, 1, - 1, 3)

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