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

The solution to (1+2i)(2-i)(1+i) is 1+7i

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

simplify

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

1 + 7 i

Solution steps

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

Apply complex arithmetic rule:

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

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

Apply complex arithmetic rule:

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

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

Simplify

((1 \cdot 2 - 2 (- 1)) \cdot 1 - (1 \cdot (- 1) + 2 \cdot 2) \cdot 1) + ((1 \cdot 2 - 2 (- 1)) \cdot 1 + (1 \cdot (- 1) + 2 \cdot 2) \cdot 1) i : 1 + 7 i

= 1 + 7 i

\frac{72 a ^{8}}{b ^{2}}

(- 3 a^{2} b^{4} c^{6})^{2}

- 9 (- 8 m - 5 m + 1) - 9 m

1 + \frac{x}{1 + \frac{1}{x}}

- 7 \cdot (- 8)