# How do you divide #( i-3) / (7i +3)# in trigonometric form?

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To divide complex numbers in trigonometric form, we first express the complex numbers in polar form. Then, we divide their magnitudes and subtract their arguments.

Given ((i - 3) / (7i + 3)), we express these complex numbers in polar form:

(i - 3 = \sqrt{1^2 + (-3)^2} \angle \tan^{-1}(\frac{-3}{1}) = \sqrt{10} \angle -71.57^\circ)

(7i + 3 = \sqrt{7^2 + 3^2} \angle \tan^{-1}(\frac{3}{7}) = \sqrt{58} \angle 22.62^\circ)

Now, divide their magnitudes and subtract their arguments:

[\frac{\sqrt{10}}{\sqrt{58}} \angle (-71.57^\circ - 22.62^\circ)]

[\frac{\sqrt{10}}{\sqrt{58}} \angle -94.19^\circ]

So, ((i - 3) / (7i + 3)) in trigonometric form is (\frac{\sqrt{10}}{\sqrt{58}} \angle -94.19^\circ).

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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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