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.

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