How do you convert #2  2i# to polar form?
here x = 2 and y = 2
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To convert (2  2i) to polar form, follow these steps:
 Find the magnitude (or absolute value) of the complex number using the formula (r = \sqrt{a^2 + b^2}), where (a) is the real part and (b) is the imaginary part.
 Find the angle (or argument) of the complex number using the formula (\theta = \arctan{\left(\frac{b}{a}\right)}), where (a) and (b) are the real and imaginary parts, respectively.
 Express the complex number in polar form as (r(\cos{\theta} + i\sin{\theta})).
Given (2  2i), where the real part (a = 2) and the imaginary part (b = 2), we can proceed as follows:

Calculate the magnitude: [ r = \sqrt{(2)^2 + (2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} ]

Calculate the angle: [ \theta = \arctan{\left(\frac{2}{2}\right)} = \arctan{(1)} ]

Determine the angle in the appropriate quadrant. Since both the real and imaginary parts are negative, the angle lies in the third quadrant, so we need to add (\pi) to the result of the arctan function. Thus: [ \theta = \arctan{(1)} + \pi = \frac{\pi}{4} + \pi = \frac{3\pi}{4} ]

Express the complex number in polar form: [ 2  2i = 2\sqrt{2} \left(\cos{\frac{3\pi}{4}} + i\sin{\frac{3\pi}{4}}\right) ]
So, the polar form of (2  2i) is (2\sqrt{2}\left(\cos{\frac{3\pi}{4}} + i\sin{\frac{3\pi}{4}}\right)).
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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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