$(1\mathrm{.}1)$ Using GNU Octave, evaluate the series

$1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-$cdots$-\frac{1}{1003}.$

$(1\mathrm{.}2)$ Use GNU Octave to plot the following graphs

a$.f(x)=xsin(x)$ in the range $-3x8.$

b$.f(x)=xcos(x^2)$ in the range $0x5.$

$(1\mathrm{.}3)$ Given a $2$ by $2$ matrix

$A=\left[\begin{array}{cc}\frac{e^{10}+i}{5e}& \frac{e^{10}-i}{5e}\\ \frac{e^{10}-i}{10e}& \frac{e^{10}+i}{5e}\end{array}\right].$

a$.$ Compute the inverse of A$.$

a$.$ Compute the complex conjugate transpose of A$.$