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

The solution to (4+3i)(4+2i)(3-i)(1-i) is 100

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

simplify

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

100

Solution steps

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

Apply complex arithmetic rule:

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

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

Apply complex arithmetic rule:

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

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

Apply complex arithmetic rule:

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

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

Simplify

(((4 \cdot 4 - 3 \cdot 2) \cdot 3 - (4 \cdot 2 + 3 \cdot 4) (- 1)) \cdot 1 - ((4 \cdot 4 - 3 \cdot 2) (- 1) + (4 \cdot 2 + 3 \cdot 4) \cdot 3) (- 1)) + (((4 \cdot 4 - 3 \cdot 2) \cdot 3 - (4 \cdot 2 + 3 \cdot 4) (- 1)) (- 1) + ((4 \cdot 4 - 3 \cdot 2) (- 1) + (4 \cdot 2 + 3 \cdot 4) \cdot 3) \cdot 1) i : 100

= 100

m^{2} - 12 m + 20

7 + 4 y = 7 - 5 y + 54

5 (x - 2) (x + 4) > 0

\frac{4}{x - 3} < 0

2^{2}