complex numbers

Let $P(z)=z^3+(1+j) z^2+(2+j) z+3$, where $z$ is complex number. Which one of the following is true?

For a complex number z, $\lim_{z \to i} \frac{z^2+1}{z^3+2z-i(z^2+2)}$ is

Consider the line integral $I = \int_C (x^2 +iy^2)dz$, where $z = x + iy$. The line $C$ is shown in the figure below. The value of $I$ is

The Fourier transform of a continuous-time signal x(t) is given by X(ω) = 1 / (10+jω)^2, -∞ < ω < ∞, where j=√-1 and ω denotes frequency. Then the value of |ln x(t)| at t =1 is ___...

All the values of the multi valued complex function $${1^i},$$ where $$i = \sqrt { - 1} $$ are

Square roots of $$-i,$$ where $$i = \sqrt { - 1} $$ are

If $$x = \sqrt { - 1} ,\,\,$$ then the value of $${X^x}$$ is

The two vectors $$\left[ {\matrix{ {1,} & {1,} & {1} \cr } } \right]$$ and $$\left[ {\matrix{ {1,} & {a,} & {{a^2}} \cr } } \right]$$ where $$a = {{ - 1} \over 2} + j{{\sqrt 3 } \o...

The two vectors $$\left[ {\matrix{ 1 & 1 & 1 \cr } } \right]$$ and $$\left[ {\matrix{ 1 & a & {{a^2}} \cr } } \right]$$ where $$a = - {1 \over 2} + j{{\sqrt 3 } \over 2}$$ and $$j...