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

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°)