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><mn>3</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mo>-</mo><mn>4</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</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> .

Add <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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 <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> produces an angle in the fourth quadrant, the value of the angle is <math><mstyle displaystyle="true"><mo>-</mo><mn>0.92729521</mn></mstyle></math> .

Substitute the values of <math><mstyle displaystyle="true"><mi>θ</mi><mo>=</mo><mo>-</mo><mn>0.92729521</mn></mstyle></math> and <math><mstyle displaystyle="true"><mrow><mo>|</mo><mi>z</mi><mo>|</mo></mrow><mo>=</mo><mn>5</mn></mstyle></math> .

Replace the right side of the equation with the trigonometric form.

Do you know how to Find All Complex Number Solutions z=3-4i? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | one billion three hundred ninety-six million six hundred one thousand eight hundred fifteen |
---|

- 1396601815 has 16 divisors, whose sum is
**1478424960** - The reverse of 1396601815 is
**5181066931** - Previous prime number is
**1579**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 40
- Digital Root 4

Name | one billion six hundred eighty-one million nine hundred thirty-three thousand six hundred fifty-eight |
---|

- 1681933658 has 8 divisors, whose sum is
**2671306452** - The reverse of 1681933658 is
**8563391861** - Previous prime number is
**17**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 50
- Digital Root 5

Name | one billion three hundred eleven million three hundred twenty-three thousand six hundred fifty-eight |
---|

- 1311323658 has 8 divisors, whose sum is
**2622647328** - The reverse of 1311323658 is
**8563231131** - Previous prime number is
**3**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 33
- Digital Root 6