Question

calculati modulul numarulu complex z=1+2i/2-i.
Urgent!!!!!!

Answer 1

z = (1 + 2i) / (2 - i)
|z| = |(1 + 2i) / ( 2 - i)| = | 1 + 2i | / | 2 - i | =$\sqrt{ 1^{2}+ 2^{2} } / \sqrt{ 2^{2}+ 1^{2} } = \sqrt{5} / \sqrt{5} =1$ 
In concluzie, modulul numarului complex este 1.

Answer 2

$z= \frac{1+2i}{2-i}= \frac{(1+2i)(2+i)}{(2-i)(2+i)} = \frac{2+i+4i+2i^2}{4-i^2} = \frac{5i}{5} =i \\ I iI= \sqrt{0^2+1^2}=1$