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

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

Popular >

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

simplify

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

- 10 i

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

Simplify

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

= - 10 i

(1 \frac{5}{7} x^{3 m - \frac{1}{3}})^{3} \cdot (\frac{7}{12} x^{\frac{1}{3}})^{3}

81 \cdot 900

- 12 \cdot 4

5 \cdot \frac{4}{5}

5^{- \frac{1}{3}}