To find the Modulus of a complex numberI was given the following expression , | ( 3 + i ) ( 2 − i ) ( 1 + i ) | and was asked to find its valueThis is how I proceeded ,On solving the numerator , the given expression transforms to | 7 − i 1 + i | Then I took the conjugate of the denominator and finally got the expression 8 − 8 i 2 = 4 | ( 1 − i ) | Now according to me it’s modulus should be 4 2 however the correct answer is 5 . Could you please correct me where I am mistaken ? And please suggest a method to solve this. Thank you .

Question

To find the Modulus of a complex numberI was given the following expression ,      |              (      3      +      i      )      (      2      −      i      )              (      1      +      i      )            |  and was asked to find its valueThis is how I proceeded ,On solving the numerator , the given expression transforms to       |              7      −      i              1      +      i            |   Then I took the conjugate of the denominator and finally got the expression            8      −      8      i        2    =  4      |    (  1  −  i  )      |  Now according to me it’s modulus should be   4      2   however the correct answer is   5 . Could you please correct me where I am mistaken ? And please suggest a method to solve this. Thank you .

Dobricap · Accepted Answer

Because      |                  (        3        +        i        )        (        2        −        i        )                    (        1        +        i        )              |    =                    10            ⋅              5                    2        =  5.

ebendasqc · Accepted Answer

(  7  −  i  )  (  1  −  i  )  ≠  8  −  8  i. So             |                  6      −      8      i        2              |        =  5Easier way to evaluate is seperating the absolute value as:            |                  (      3      +      i      )      (      2      −      i      )              (      1      +      i      )                  |        =                    |            3      +      i              |                    |            2      −      i              |                            |            1      +      i              |              =                    10            ⋅              5                    2        =  5

Answered question

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