What is (2+2i)*(1-5i)*(2+3i) ?

The solution to (2+2i)*(1-5i)*(2+3i) is 48+20i

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

simplify

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

48 + 20 i

Solution steps

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

Apply complex arithmetic rule:

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

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

Apply complex arithmetic rule:

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

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

Simplify

((2 \cdot 1 - 2 (- 5)) \cdot 2 - (2 (- 5) + 2 \cdot 1) \cdot 3) + ((2 \cdot 1 - 2 (- 5)) \cdot 3 + (2 (- 5) + 2 \cdot 1) \cdot 2) i : 48 + 20 i

= 48 + 20 i

a^{3} b^{3} + ab + a^{2} b^{2} + 1

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

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

(\frac{4 ^{3}}{y})^{3}

- 25 - - 4