1. Detormiue the complex number 2 which sat afies \( z(3+3 i)=2-i \).
2. Given that \( p \) and \( q \) are mal and that 1 t 2 is is mont of the equation \( 2^{2}+(p+5 i)=+\eta(2-i)= \) 14. Determine
(a) the valus of pausis
(b) the ather root of the aquation
3. Let \( z_{1}=1+i \) and \( s_{2}=v^{3}+i \).
(a) Find the modulus of \( s_{1}, z_{2}, z_{1} z_{2} \) and \( \frac{1}{s_{2}} \)
4. (a) Write the complex number \( :=-3+41 \mathrm{~m} \) polar lorm.
(b) Describe what happonat to the coaples number \( \{=a-b \) when multiplied toy \( \left[3 \cdot \frac{\pi}{3}\right] \) :
6. Solve the equation \( z^{3}-i(2-1)^{3} \) giving yout allswiet in the form \( a+b \) b
T. Find a closed form magrmethes for the generatime finetion for the followius sequerice
(a) \( -2,0,-2,0,-2 \),
(b) \( 1, a, a^{2}, a^{3}, \ldots \)
(c) \( 0.1,-\frac{1}{2}, \frac{1}{3},-\frac{1}{4} \)
