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

The solution to (1+i)(2+3i)(4-3i) is 11+23i

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

simplify

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

11 + 23 i

Solution steps

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

Simplify

((1 \cdot 2 - 1 \cdot 3) \cdot 4 - (1 \cdot 3 + 1 \cdot 2) (- 3)) + ((1 \cdot 2 - 1 \cdot 3) (- 3) + (1 \cdot 3 + 1 \cdot 2) \cdot 4) i : 11 + 23 i

= 11 + 23 i

\frac{14}{30}

e^{1.7}

\frac{2}{5 x} + \frac{1}{x}

\frac{9 !}{4 ! 5 !}

\frac{1}{3} \cdot (- 1)