Section 1
Test exercise F.2
\text { Express in polar form, } z=-5-j 3
Express in the form $a+j b$ :(a) $2\left\lfloor 156^{\circ}\right.$(b) $5 \longdiv { 3 7 ^ { \circ } }$
If $z_{1}=12\left(\cos 125^{\circ}+j \sin 125^{\circ}\right)$ and $z_{2}=3\left(\cos 72^{\circ}+j \sin 72^{\circ}\right)$, find (a) $z_{1} z_{2}$ and (b) $\frac{z_{1}}{z_{2}}$ giving the results in polar form.
If $z=2\left(\cos 25^{\circ}+j \sin 25^{\circ}\right)$, find $z^{3}$ in polar form.
Find the three cube roots of $8\left(\cos 264^{\circ}+j \sin 264^{\circ}\right)$ and state which of them is the principal cube root. Show all three roots on an Argand diagram.
Expand $\sin 4 \theta$ in powers of $\sin \theta$ and $\cos \theta$.
Express $\cos ^{4} \theta$ in terms of cosines of multiples of $\theta$.
If $z=x+i y$, find the equations of the two loci defined by:(a) $|z-4|=3$(b) $\arg (z+2)=\frac{\pi}{6}$