Question

PLS HELPPP
Express the complex number in trigonometric form.

3 - 3i

Answer 1

z = a + bi
z = 3 - 3i

|z| = √(a² + b²)
|3 - 3i| = √(3² + 3²)
|3 - 3i| = √(9 + 9)
|3 - 3i| = √(18)
|3 - 3i| = √(9 × 2)
|3 - 3i| = √(9)√(2)
|3 - 3i| = 3√(2)

tanΘ = b/a
tanΘ = ⁻³/₃
tanΘ = -1

Θ = arctan(-1)
Θ ≈ -0.8

z = 3√(2)(cos(-0.8) + i sin(-0.8))