How do you multiply # (1+3i)(13i) # in trigonometric form?
#(1 + 3i)(1  3i) = 10#
So:
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To multiply ( (1+3i)(13i) ) in trigonometric form, follow these steps:
 Rewrite each complex number in polar form.
 Multiply the magnitudes and add the angles.
 Convert the result back to rectangular form if needed.
Let's break it down:

Convert ( 1+3i ) and ( 13i ) into polar form: ( 1+3i = \sqrt{1^2 + 3^2} \cdot e^{i \arctan(3/1)} = \sqrt{10} \cdot e^{i \arctan(3)} ) ( 13i = \sqrt{1^2 + (3)^2} \cdot e^{i \arctan(3/1)} = \sqrt{10} \cdot e^{i \arctan(3)} )

Multiply the magnitudes and add the angles: ( \sqrt{10} \cdot e^{i \arctan(3)} \cdot \sqrt{10} \cdot e^{i \arctan(3)} ) ( = 10 \cdot e^{i (\arctan(3) + \arctan(3))} ) ( = 10 \cdot e^{i (\arctan(3)  \arctan(3))} ) ( = 10 \cdot e^{i \cdot 0} ) ( = 10 )
So, ( (1+3i)(13i) ) in trigonometric form is ( 10 ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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