What is (2-i)(3+2i)(1-4i) ?

The solution to (2-i)(3+2i)(1-4i) is 12-31i

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simplify (2-i)(3+2i)(1-4i)

simplify

(2 - i) (3 + 2 i) (1 - 4 i)

12 - 31 i

Solution steps

(2 - i) (3 + 2 i) (1 - 4 i)

Apply complex arithmetic rule:

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

= ((2 \cdot 3 - (- 1) \cdot 2) + (2 \cdot 2 - 1 \cdot 3) i) (1 - 4 i)

Apply complex arithmetic rule:

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

= ((2 \cdot 3 - (- 1) \cdot 2) \cdot 1 - (2 \cdot 2 - 1 \cdot 3) (- 4)) + ((2 \cdot 3 - (- 1) \cdot 2) (- 4) + (2 \cdot 2 - 1 \cdot 3) \cdot 1) i

Simplify

((2 \cdot 3 - (- 1) \cdot 2) \cdot 1 - (2 \cdot 2 - 1 \cdot 3) (- 4)) + ((2 \cdot 3 - (- 1) \cdot 2) (- 4) + (2 \cdot 2 - 1 \cdot 3) \cdot 1) i : 12 - 31 i

= 12 - 31 i

\frac{4}{3} \div \frac{7}{4}

- (- 6.5 g + 3)

327

- 2 x^{2} + 6 x + 56

(5 x^{2} - 2)^{4}