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 | three hundred twenty-three million nine hundred eighty-nine thousand nine hundred thirty-nine |
---|

- 323989939 has 4 divisors, whose sum is
**327550360** - The reverse of 323989939 is
**939989323** - Previous prime number is
**91**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 55
- Digital Root 1

Name | one billion eight hundred fifty-two million eight hundred thirteen thousand eight hundred twenty-seven |
---|

- 1852813827 has 8 divisors, whose sum is
**2074398480** - The reverse of 1852813827 is
**7283182581** - Previous prime number is
**131**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 45
- Digital Root 9

Name | seventy million ninety-three thousand nine hundred fifty-four |
---|

- 70093954 has 8 divisors, whose sum is
**120161088** - The reverse of 70093954 is
**45939007** - Previous prime number is
**7**

- Is Prime? no
- Number parity even
- Number length 8
- Sum of Digits 37
- Digital Root 1