Question

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Answer 1

Answer:

2π/3

Step-by-step explanation:

Given,

z = (1 + i√3)²

⇒ 1² + (√3i)² + 2 * 1 * √3i

⇒ 1 + 3i² + 2i√3

⇒ 1 - 3 + 2i√3[∵i² = -1]

⇒ -2 + 2i√3

From this Let,

a = -2, b = 2√3

Then,

tanα = |b/a|

⇒ tanα = |2√3/-2|

⇒ tanα = |-√3|

⇒ α = 60° or π/3

∴ z lies in 2nd  quadrant.

arg(z) = θ

⇒ π - α

⇒ π - π/3

⇒ 2π/3

Hope it helps!