How do you write the trigonometric form of 52(3−i)?

Madilyn Fitzgerald

Madilyn Fitzgerald

Answered

2022-02-01

How do you write the trigonometric form of 52(3i)?

Answer & Explanation

Troy Sutton

Troy Sutton

Expert

2022-02-02Added 13 answers

Answer: 5(cos(π6)+isin(π6))
Explanation:
The trigonometric form of a complex number z=a+ib is
z=|z|(cosθ+isinθ)
where cosθ=a|z|
and sinθ=b|z|
Here z=52(3i)
|z|=523+1=522=5
z=5(3212i)
cosθ=32
sinθ=12
θ=π6,[mod2π]
The trigonometric form is
z=5(cos(π6)+isin(π6))=5eiπ6

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