Complex numbers problem

[mathwannabe]

Hello everybody

I got this problem, I just can't figure it out... I spent too much time on it and have failed, so I am asking for help

1)The value of the expression \(\displaystyle |\dfrac{1-z}{1+z}|\) for \(\displaystyle z=2i\)

I got to \(\displaystyle |\dfrac{-3-4i}{5}|\), but the correct answer should be 1. I have no idea how to get there. Hint?

 

[pka]

1)The value of the expression \(\displaystyle |\dfrac{1-z}{1+z}|\) for \(\displaystyle z=2i\)

I got to \(\displaystyle |\dfrac{-3-4i}{5}|\), but the correct answer should be 1. I have no idea how to get there.

\(\displaystyle |-3-4i|=\sqrt{(-3)^2+(-4)^2}\)

 

[soroban]

Hello, mathwannabe!

I got this problem, I just can't figure it out..

(1) The value of the expression \(\displaystyle \left|\dfrac{1-z}{1+z}\right|\) for \(\displaystyle z=2i\)

I got to \(\displaystyle \left|\dfrac{\text{-}3-4i}{5}\right|\), but the correct answer should be 1.

Do you understand what those vertical lines mean?

The magnitude of \(\displaystyle a + bi\) is: .\(\displaystyle \big|a + bi\big| \;=\;\sqrt{a^2+b^2}\)


We have: .\(\displaystyle \left|\text{-}\frac{3}{5} - \frac{4}{5}i\right| \;=\;\sqrt{\left(\text{-}\frac{3}{5}\right)^2 + \left(\text{-}\frac{4}{5}\right)^2}\)


. . . . . . . . . . . . . . . . \(\displaystyle =\;\sqrt{\frac{9}{25} + \frac{16}{25}} \;=\;\sqrt{\frac{25}{25}} \;=\;\sqrt{1} \;=\;1\)

 

[mathwannabe]

Hello, mathwannabe!


Do you understand what those vertical lines mean?

The magnitude of \(\displaystyle a + bi\) is: .\(\displaystyle \big|a + bi\big| \;=\;\sqrt{a^2+b^2}\)


We have: .\(\displaystyle \left|\text{-}\frac{3}{5} - \frac{4}{5}i\right| \;=\;\sqrt{\left(\text{-}\frac{3}{5}\right)^2 + \left(\text{-}\frac{4}{5}\right)^2}\)


. . . . . . . . . . . . . . . . \(\displaystyle =\;\sqrt{\frac{9}{25} + \frac{16}{25}} \;=\;\sqrt{\frac{25}{25}} \;=\;\sqrt{1} \;=\;1\)

Yes... Moduo or absolute value of complex number. Thank you for this reply, it pointed me in the right direction.

 

[Deleted member 4993]

Yes... Moduo or absolute value of complex number. Thank you for this reply, it pointed me in the right direction.

Pointed .... it SPOON_FED you the whole answer - nothing but the whole answer.

 

[mathwannabe]

Pointed .... it SPOON_FED you the whole answer - nothing but the whole answer.

Can't argue with that Now I feel like I have a nasal feeding tube installed...