Trigonometric Form of Complex Numbers Calculator

Complex number is the combination of real and imaginary number. It can be written in the form a + bi. Here, both m and n are real numbers, while i is the imaginary number. We can convert the complex number into trigonometric form by finding the modulus and argument of the complex number. Use this online calculator to find the trigonometric form of the given complex number by providing the real and complex numbers.

Convert Complex Numbers to Trigonometric Form

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i
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Formula:

z = a + bi = |z| (cosθ + isinθ) θ = arctan(b / a)

Note: if (+b / +a) = > θ = θ if (+b / -a) = > θ = 180 - θ if (-b / -a) = > θ = 180 + θ if (-b / +a) = > θ = 360 - θ

Where, z = Trigonometric Form a = Real Value b = Imaginary Value θ = Angle |z| = Modulus

Example

Convert complex numbers a = 2 and b = 6 to trigonometric form
z = a + bi =|z|(cosθ + isinθ)
θ = arctan(b / a)
θ = arctan (2 / 6) = 0.1845
z = 2 + 6i
|z| = √(4 + 36)
|z| = √40
|z| = 6.324
Trig form = 6.3246 (cos (71.5651) + i sin (71.5651))

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