Question

Write 1 +✓-3i in polar form

Answer 1

Answer:

z=1+√-3i

|z|=√(1)^2+(√-3)^2=√1+3=√4=2

Step-by-step explanation:

2(cosπ/3+isinπ/3)

Answer 2

Answer:

z = 1 - √3 i

|z| = r = √(1² + √(-3)²)

⇒ r = √(1 + 3) = 2

r cos ∅ = 1, r sin ∅ = -√3

cos ∅ = 1/2, sin ∅ = -√3/2

Now, ∅ lies in fourth quadrant.

So, ∅ = -π/3

Polar form : r(cos ∅ + i sin ∅)

Hence, 2(cos (-π/3) + i sin (-π/3))

SOME IMPORTANT FORMULAS :

1. r = √(x² + y²)
2. cos ∅ = x/r
3. sin ∅ = y/r
4. i^{4k} = 1
5. i^{4k + 1} = i
6. i^{4k + 2} = - 1
7. i^{4k + 3} = - i
8. z_1 + z_2 = (a + c) + i (b + d)
9. z_1 × z_2 = (ac - bd) + i (ad + bc)