This is the trigonometric form of a complex number where <math><mstyle displaystyle="true"><mrow><mo>|</mo><mi>z</mi><mo>|</mo></mrow></mstyle></math> is the modulus and <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> is the angle created on the complex plane.

The modulus of a complex number is the distance from the origin on the complex plane.

Substitute the actual values of <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><msqrt><mn>3</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>3</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>3</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate the exponent.

Add <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>3</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

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 <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> produces an angle in the first quadrant, the value of the angle is <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

Substitute the values of <math><mstyle displaystyle="true"><mi>θ</mi><mo>=</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mrow><mo>|</mo><mi>z</mi><mo>|</mo></mrow><mo>=</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></mstyle></math> .

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Name | one billion six hundred ninety million one hundred thirty-eight thousand eight hundred ninety-nine |
---|

- 1690138899 has 8 divisors, whose sum is
**1753481520** - The reverse of 1690138899 is
**9988310961** - Previous prime number is
**23993**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 54
- Digital Root 9

Name | one billion two hundred eighty million three hundred ninety-seven thousand nine hundred twenty-eight |
---|

- 1280397928 has 32 divisors, whose sum is
**4421840544** - The reverse of 1280397928 is
**8297930821** - Previous prime number is
**43**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 49
- Digital Root 4

Name | three hundred twenty million nine hundred eighty-two thousand fifty-one |
---|

- 320982051 has 4 divisors, whose sum is
**329212400** - The reverse of 320982051 is
**150289023** - Previous prime number is
**39**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 30
- Digital Root 3