How do you find the trigonometric form of a complex number?

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How do you find the trigonometric form of a complex number?

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Answer 1 · 2018-06-14T06:57:23

As detailed below.

Explanation:

Trigonometric Form of a Complex Number. The trigonometric form of a complex number z = a + bi is. z = r(cos θ + i sin θ), where r = |a + bi| is the modulus of z, and tan θ = b. a.

Let the complex number be $z = (x + i y)$ $z = (x + i y)$

Polar form is $(r, θ)$ $(r, theta)$

$r = ∣ ∣ ∣ \sqrt{x^{2} + y^{2}} ∣ ∣ ∣$ $r = | sqrt(x^2 + y^2)|$

$θ = arctan (\frac{y}{x})$ $theta = arctan (y/x)$

Trigonometric form $= r (cos θ + i sin θ)$ $= r (cos theta + i sin theta)$

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How do you find the trigonometric form of a complex number?

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