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 | six hundred ninety million eight hundred sixty thousand two |
---|

- 690860002 has 16 divisors, whose sum is
**1184702400** - The reverse of 690860002 is
**200068096** - Previous prime number is
**4507**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 31
- Digital Root 4

Name | one billion one hundred fifty-four million two hundred sixty-eight thousand six hundred forty-two |
---|

- 1154268642 has 32 divisors, whose sum is
**2323455552** - The reverse of 1154268642 is
**2468624511** - Previous prime number is
**1627**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 39
- Digital Root 3

Name | one billion seven hundred thirty-five million four hundred seventy-two thousand nine |
---|

- 1735472009 has 4 divisors, whose sum is
**1737948420** - The reverse of 1735472009 is
**9002745371** - Previous prime number is
**701**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 38
- Digital Root 2