The polar form of a vector is 10∠30. What is the rectangular form of this vector?

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  1. \(\rm 10\sqrt3 + j2\)
  2. \(\rm 5\sqrt3 + j5\)
  3. \(\rm \sqrt3 + j5\)
  4. \(\rm 15\sqrt3 + j3\)

Answer (Detailed Solution Below)

Option 2 : \(\rm 5\sqrt3 + j5\)
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Detailed Solution

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Conversion from polar to rectangular form

The polar form of a coordinate is represented by \(a∠\theta\)

The rectangular form of a coordinate is represented by \(x+iy\)

where, \(x=acos\theta\)

\(y=asin\theta\)

Calculation

Given, Polar form:  10∠30° 

The rectangular form is given by:

x = 10 cos(30°)

x = \(\rm 5√3 \)

y = 10 sin(30°)

y = 5

 The rectangular form is 5√3 + j5

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