QUESTION $2$

a$.$ Find the following integrals:

i$.,{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}13si{n}^2(4x)dx$

ii$.,{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}10si{n}^5(2x+1)dx$

iii. ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}9sin(5x)cos(2x)dx$

$[4+6+4$ marks$]$

b$.$ Given the complex numbers $z_1=2-3j,z_2=-3j$ and $z_3=5+j,$ express the following in the form $a+bj$; where $a,$bin$$ and $j^2=-1$ :

i$.,z_2{z}_3$

ii$.\frac{z_1}{z_3}$

$[2+4$ marks$]$

$[$Total marks $20]$