# How do you convert #1 - 3i# to polar form?

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To convert the complex number (1 - 3i) to polar form, we need to find its magnitude (absolute value) and argument (angle).

The magnitude (r) of a complex number (a + bi) is given by the formula:

[ r = |a + bi| = \sqrt{a^2 + b^2} ]

In this case, (a = 1) and (b = -3). Substituting these values into the formula:

[ r = \sqrt{1^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} ]

So, the magnitude of (1 - 3i) is ( \sqrt{10} ).

The argument (\theta) of a complex number (a + bi) can be found using the formula:

[ \theta = \text{arctan}\left(\frac{b}{a}\right) ]

In this case, (a = 1) and (b = -3). Substituting these values into the formula:

[ \theta = \text{arctan}\left(\frac{-3}{1}\right) = \text{arctan}(-3) ]

Using a calculator, we find that ( \text{arctan}(-3) \approx -1.249 ) radians.

Therefore, the polar form of (1 - 3i) is ( \sqrt{10} , \text{cis}(-1.249) ), where cis represents the complex exponential form.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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