What is (1+2i)(5+3i)(4+i) ?

The solution to (1+2i)(5+3i)(4+i) is -17+51i

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simplify (1+2i)(5+3i)(4+i)

simplify

(1 + 2 i) (5 + 3 i) (4 + i)

- 17 + 51 i

Solution steps

(1 + 2 i) (5 + 3 i) (4 + i)

Apply complex arithmetic rule:

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

= ((1 \cdot 5 - 2 \cdot 3) + (1 \cdot 3 + 2 \cdot 5) i) (4 + i)

Apply complex arithmetic rule:

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

= ((1 \cdot 5 - 2 \cdot 3) \cdot 4 - (1 \cdot 3 + 2 \cdot 5) \cdot 1) + ((1 \cdot 5 - 2 \cdot 3) \cdot 1 + (1 \cdot 3 + 2 \cdot 5) \cdot 4) i

Simplify

((1 \cdot 5 - 2 \cdot 3) \cdot 4 - (1 \cdot 3 + 2 \cdot 5) \cdot 1) + ((1 \cdot 5 - 2 \cdot 3) \cdot 1 + (1 \cdot 3 + 2 \cdot 5) \cdot 4) i : - 17 + 51 i

= - 17 + 51 i

2 x^{3} \cdot 2 x

2 x^{3} \cdot 3 x

(- 6) (4)

2 (x - 3) - 3 (x^{2} + 2 x - 4)

(3 y^{4})^{3} + 2 y^{7} - 4 y^{12}