Convert to Trigonometric Form 3(cos(pi)+isin(pi))

Convert to Trigonometric Form 3(cos(pi)+isin(pi))
Simplify each term.
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Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
The exact value of is .
Multiply by .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Multiply by .
Simplify the expression.
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Add and .
Multiply by .
This is the trigonometric form of a complex number where is the modulus and is the angle created on the complex plane.
The modulus of a complex number is the distance from the origin on the complex plane.
where
Substitute the actual values of and .
Find .
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Raising to any positive power yields .
Raise to the power of .
Add and .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
Since inverse tangent of produces an angle in the second quadrant, the value of the angle is .
Substitute the values of and .
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Name

Name two hundred forty-two million five hundred forty-seven thousand one hundred seventy-two

Interesting facts

  • 242547172 has 64 divisors, whose sum is 638720640
  • The reverse of 242547172 is 271745242
  • Previous prime number is 73

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 34
  • Digital Root 7

Name

Name one billion two hundred twenty million three hundred sixteen thousand eight hundred thirty-one

Interesting facts

  • 1220316831 has 16 divisors, whose sum is 1455900480
  • The reverse of 1220316831 is 1386130221
  • Previous prime number is 71

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 27
  • Digital Root 9

Name

Name one billion eight hundred twenty-one million five hundred seventy-eight thousand five hundred forty-six

Interesting facts

  • 1821578546 has 4 divisors, whose sum is 2732367822
  • The reverse of 1821578546 is 6458751281
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 47
  • Digital Root 2