Question

Multiple choice: 
Express the complex number in trigonometric form. -2 Even if you guess its probably better than my guess

 2(cos 90° + i sin 90°)  
2(cos 0° + i sin 0°) 
2(cos 180° + i sin 180°)  
2(cos 270° + i sin 270°)

Even if you guess its probably better than my guess

Answer 1

In the given you wrote -2, whereas it should be -2i

z = a + bi and in trigo form | z |.(cos Ф + i.sin Ф).
z = 0 -2i → | z |.(cos Ф + i.sin Ф)
Now let's calculate z:
 
z² = a²+b² → z² = 0² (-2.i)² → z = -2(i)² →z= -2(-1) → z = |2|
tan Ф = b/a = -2/0 → tan Ф → - ∞ ↔ Ф = -90° or Ф = 270°
 then the - 2 I ↔ |2|(cos 270° + i.sin 270°)