Given $z=3-4j$

i$.$ Represent $z$ on an flyand Diagram showing coordindtes & mo dulus and argument $$ of $z$

ii$.$ Express $z$ in polar form with arg$$ in terms of $$

$($use the principle value & argument to $2$ decimel places correctly$)$

iii Hence find the value of $z^3$ in polar Using de movier's theorem

iv$.$ Give the answer to part

o $($iii$)$ in cartesian form

v$.$ Obtain the $4$ solutions of the equation

$z^4=3-4j$

& display the roots on an argand

$4.$ A tank contains $30$ litres of 'a Solution of a chemical in water. The amount of the chemical at the beginning is $60$ grams. The

concentration of the chemical concentration of the chemical is reduced by running wemer

pure water into the tank pure water into the tank at a rate of $2$ litres per minute. The tank contains $S$ gramis of chemical at time $t$ minutes after the dilution starts.

a$.$ What is the Volume of the polluted water of the tank at any time $t?$

b$.$ Determine the time to empry the tank

C$.$ Construct a a differential equation Showing the connection of ratte of

change of the amount of chemical change of the amount of chemical in the Tank $($s$)$ & time $(t)$

$\text{'}$d$.$ Solve the differential equation to find the amount of chemicall $S$ in terms of $t$ use it to find the fraction of the original chemial still in the tank after $20$ minutes.

$2$