Question

z=2+6√3i/5+√3i simplify ​

Answer 1

Answer:

2(cos 60+ isin 60)

step by step

z = (2+ i6√3)*(5 - i√3) / (5 + i√3)*(5 - i√3)

z = (10 - 2i√3 + 30i√3 - 6i² *3) / (25 - 3i²) , i² = -1

z = (28 + 28i√3) / 28

z = 1 + i√3

In polar form:

z = r*(cosθ + i sinθ)

r =IzI = √((1²+(√3)²) = √4 = 2

tanθ = √3/1 = √3

θ = 60°

z = 2*(cos60° + i sin60°)