Here’s an interesting and doable STEP question on complex numbers (STEP 3 1996). Unlike most STEP questions, this one is doable: Not that hard to figure out, but still needs some thought. Give it a try!
Knowledge you probably need (But not MUSTs):
- Solving Trignometry Equation
- De Moivre’s Theorem
- Vieta’s formulas for cubic polynomials
Looking for the solution?
Answer: (i) root 7 (ii) 5
I made a detailed solution to this problem in a powerpoint. You can view it here: step3_1996_Q5_solution