What is the absolute value of: (1 + i) (6 + 2i)/ (4 + i) (9 + 3i)

 

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We have to find the absolute value of (1 + i) (6 + 2i)/ (4 + i) (9 + 3i). First we convert it to a form x+iy and then use the formula sqrt(x^2 + y^2) to determine the absolute value.

(1 + i)(6 + 2i)/ (4 + i) (9 + 3i)

=> (1 + i)(6 + 2i)(4 - i)(9 - 3i)/(4 + i)(9 + 3i)(4 - i)(9 - 3i)

=> (1 + i) (6 + 2i) (4 - i) (9 - 3i)/ (4^2 + 1^2) (9^2 + 3^2)

=> (6 + 6i + 2i^2 + 2i) (36 – 12i – 9i + 3i^2)/ (16 +1) (81 + 9)

=> (4 + 8i) (33 – 21i)/17*90

=> [4*33 + 8*33i – 84i – 21*8*i^2] / 17*90

=> [300 + 180i]/17*90

=> [10/51 + 2i/17]

The absolute value is sqrt [(10/51) ^2 + (2/17) ^2]

=> 0.2286

The absolute value is 0.2286

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