Write the complex number in trigonometric form r(cos theta + i sin theta),with theta in the interval [0^@, 360^@]5sqrt3 + 5i

defazajx 2021-02-15 Answered

Write the complex number in trigonometric form r(cosθ+isinθ),with theta in the interval [0,360]
53+5i

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pierretteA
Answered 2021-02-16 Author has 102 answers
The trigonometric form of the complex number is r(cosθ+isinθ).
Here, r is the modulus of the complex number and theta is called the argument of the complex number.
The formula for the modulus of any complex number a+bi is defined as, r=a2+b2
Substitute a=53,b=5 in the formula for modulus.
r=(53)2+52=75+25=100=10
Since r is the modulus, it is always positive. So, r= 10.
The formula for the argument of the complex number is defined as, θ=tan1(ba)
Substitute a=53,b=5 in the formula for argument
θ=tan1(553)=tan1(13)
The value of tan is 13 for π6
So, θ=π6
So, the trigonometric form of the given complex number is 10(cos(π6)+isin(π6)
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