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

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

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

simplify

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

- 10

Solution steps

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

Apply complex arithmetic rule:

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

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

Apply complex arithmetic rule:

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

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

Simplify

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

= - 10

\frac{3 a - b}{2} + \frac{3 a - b}{5}

\frac{3}{5} x + x

(\frac{0.1}{0.01}) + 0.001

e^{2 l n (t)}

1.0 6^{12}