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Write the complex number in trigonometric form

A) $r(\cos \theta + i \sin \theta)$
B) $r(\cos \theta - i \sin \theta)$
C) $r(\cos \theta + \sin \theta)$
D) $r(\cos \theta - \sin \theta)$

User Dronir
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1 Answer

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Final Answer:

The complex number in trigonometric form is A)
$r(\cos \theta + i \sin \theta)$.

Explaination:

To represent a complex number in trigonometric form, we utilize Euler's formula:
$z = r(\cos \theta + i \sin \theta)$, where
$z$ is the complex number,
$r$ is the magnitude, and
$\theta$ is the angle.

In this case, the form A)
$r(\cos \theta + i \sin \theta)$ corresponds to the standard form of a complex number in trigonometric notation. The expression
$\cos \theta + i \sin \theta$ is derived from Euler's formula, which relates complex numbers to trigonometric functions. Here,
$\cos \theta$ represents the real part of the complex number, and
$\sin \theta$ represents the imaginary part, combined with the angle
$\theta$.

The use of
$\cos \theta + i \sin \theta$ represents the magnitude
$r$ along with the angle
$\theta$ in the complex plane. It is a concise and standard way of expressing complex numbers, highlighting both magnitude and direction in terms of trigonometric functions, making it a convenient form for various mathematical operations and analyses involving complex numbers.

User Lion
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