The modulus of the complex number \(\left( {\frac{{3 + 4i}}{{1 - 2i}}} \right)\) is
\(\sqrt 5\)
The modulus of a quotient is the quotient of moduli: |3+4i|/|1−2i|=5/√5=√5.
The contour integral $$\oint_C e^{1/z} dz$$ with C as the counter-clockwise unit circle in the z-plane is equal to
Let $$ I = \int_0^1 \frac{1}{1+t} dt + \frac{\pi i}{2} \int_0^1 \frac{1}{1+e^2} dt - i \int_0^1 \frac{1}{1+it} dt, $$ where $ t $ is a real variable and $ i = \sqrt{-1} $. The value of $ I $ is ______________