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

The solution to (1-2i)(3+2i)(5+2i) is 43-6i

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

simplify

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

43 - 6 i

Solution steps

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

Apply complex arithmetic rule:

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

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

Apply complex arithmetic rule:

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

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

Simplify

((1 \cdot 3 - (- 2) \cdot 2) \cdot 5 - (1 \cdot 2 - 2 \cdot 3) \cdot 2) + ((1 \cdot 3 - (- 2) \cdot 2) \cdot 2 + (1 \cdot 2 - 2 \cdot 3) \cdot 5) i : 43 - 6 i

= 43 - 6 i

\frac{x ^{4} - y ^{4}}{x ^{2} - y ^{2}}

\frac{( 2 n ) !}{( 2 n + 1 ) !}

(a + b) (2 a + 3 b) (2 x - y)

\frac{3}{14}

7 (x + 3)