1. The problem statement, all variables and given/known data Let z= √3 -i and w= 1+i i)calculate zw in "a+ib"form ii)Write z and w in polar form and thus write zw in polar form iii)Hence express tan (pi/12) in surd form. 2. Relevant equations 3. The attempt at a solution (√3 -i)(1+i) = (√3+1)+(√3i-i) ii) |z|=2 → Arg(z)=tan^-1(√3/-1) = -pi/3 so z = 2*e^-i(pi/3) |w|= √2 → Arg(w)=pi/4 so w=√2 *e^i(pi/4) so zw= 2√2*e^i(pi/4 -pi/3) = √8*e^-i(pi/12) iii) this is the part I'm having trouble with... so I think I should convert it into "a +ib" form so |zw| = √8 → Arg(zw)=-pi/12 but then Im stuck because there is no exact result for -pi/12 ????