What is (1+i)(2-i)(3-i) ?

The solution to (1+i)(2-i)(3-i) is 10

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simplify (1+i)(2-i)(3-i)

simplify

(1 + i) (2 - i) (3 - i)

10

Solution steps

(1 + i) (2 - i) (3 - i)

Apply complex arithmetic rule:

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

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

Apply complex arithmetic rule:

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

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

Simplify

((1 \cdot 2 - 1 \cdot (- 1)) \cdot 3 - (1 \cdot (- 1) + 1 \cdot 2) (- 1)) + ((1 \cdot 2 - 1 \cdot (- 1)) (- 1) + (1 \cdot (- 1) + 1 \cdot 2) \cdot 3) i : 10

= 10

\frac{x ^{6} - 8}{x ^{2} - 2}

\frac{18 x ^{3} y ^{5}}{2 y} \cdot \frac{x y ^{2}}{3 x ^{3} y ^{7}}

\frac{5}{6} \cdot \frac{3}{5}

\frac{112}{3}