# Thread: modulus

1. ## modulus

Lets say P and Q are both complex numbers . The modulus of P and Q are 1 and 2 respectively .

The question is find the modulus for the complex numbers a , b and c with

$\displaystyle a=p^4$ ,$\displaystyle b=q^2$ , $\displaystyle c=-ip$

so $\displaystyle |a|=|p|^4 = 1^4 =1$

$\displaystyle |b|=|q|^2 = 2^2$

Am i right in saying that ???

2. Originally Posted by thereddevils
Lets say P and Q are both complex numbers . The modulus of P and Q are 1 and 2 respectively .

The question is find the modulus for the complex numbers a , b and c with

$\displaystyle a=p^4$ ,$\displaystyle b=q^2$ , $\displaystyle c=-ip$

so $\displaystyle |a|=|p|^4 = 1^4 =1$

$\displaystyle |b|=|q|^2 = 2^2$

Am i right in saying that ???
it is right

for $\displaystyle c=-ip$ suppose that $\displaystyle p=x+iy$ so $\displaystyle \mid p \mid =\sqrt{x^2+y^2}=1$

$\displaystyle \mid c\mid =\mid -i(x+iy) \mid = \mid -ix+y \mid = \sqrt{(-x)^2+y^2}=\sqrt{x^2+y^2} =1$ from above

3. Originally Posted by Amer
$\displaystyle \mid c\mid =\mid -i(x+iy) \mid = \mid -ix+y \mid = \sqrt{(-x)^2+y^2}=\sqrt{x^2+y^2} =1$ from above
Why not just notice that $\displaystyle \left| {wz} \right| = \left| w \right|\left| z \right|\, \Rightarrow \,\left| { - ip} \right| = \left| { - i} \right|\left| p \right| = \left| p \right|$?