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Digital SAT
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Finding Polar Form of a Complex Number

Hard Additional Math Topics Complex Numbers

Given the complex number $z = 3 + 4i$, calculate the magnitude of $z$ and then express $z$ in polar form. The magnitude of a complex number $a + bi$ is calculated using the formula:

$$|z| = ext{sqrt}(a^2 + b^2)$$

Once you find the magnitude, the polar form is represented as:

$$z = r( ext{cos} \theta + i \sin \theta)$$

where $r$ is the magnitude you found and $\theta$ is the argument of the complex number, given by:

$$\theta = \tan^{-1}\left(\frac{b}{a}\right)$$

What is the polar form of the complex number $z$?

Hint

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