# To find the Modulus of a complex number I was given the following expression , |((3+i)(2-i))/((1+i))| and was asked to find its value This 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 (8-8i)/(2) =4|(1−i)| Now according to me it’s modulus should be 4 sqrt(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 .

Elise Kelley 2022-10-17 Answered
To find the Modulus of a complex number
I was given the following expression ,
$|\frac{\left(3+i\right)\left(2-i\right)}{\left(1+i\right)}|$
and was asked to find its value
This is how I proceeded ,
On solving the numerator , the given expression transforms to $|\frac{7-i}{1+i}|$ Then I took the conjugate of the denominator and finally got the expression
$\frac{8-8i}{2}$
$=4|\left(1-i\right)|$
Now according to me it’s modulus should be $4\sqrt{2}$ 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 .
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Dobricap
Because
$|\frac{\left(3+i\right)\left(2-i\right)}{\left(1+i\right)}|=\frac{\sqrt{10}\cdot \sqrt{5}}{\sqrt{2}}=5.$
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ebendasqc
$\left(7-i\right)\left(1-i\right)\ne 8-8i$. So $|\frac{6-8i}{2}|=5$
Easier way to evaluate is seperating the absolute value as:
$|\frac{\left(3+i\right)\left(2-i\right)}{\left(1+i\right)}|=\frac{|3+i||2-i|}{|1+i|}=\frac{\sqrt{10}\cdot \sqrt{5}}{\sqrt{2}}=5$