# How do you write #2 +4i# in trigonometric form?

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To write the complex number (2 + 4i) in trigonometric form, we need to express it in terms of its magnitude and argument.

First, we find the magnitude ((r)) 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 of the complex number.

Given (a = 2) and (b = 4), we have: [ r = \sqrt{2^2 + 4^2} = \sqrt{4 + 16} = \sqrt{20} = 2\sqrt{5} ]

Next, we find the argument ((\theta)) of the complex number using the formula: [ \theta = \arctan\left(\frac{b}{a}\right) ] where (a) is the real part and (b) is the imaginary part of the complex number.

Given (a = 2) and (b = 4), we have: [ \theta = \arctan\left(\frac{4}{2}\right) = \arctan(2) ]

Now, to express (\theta) in radians: [ \theta \approx 1.107 , \text{radians} ]

Therefore, the trigonometric form of the complex number (2 + 4i) is: [ 2\sqrt{5} \left(\cos(1.107) + i \sin(1.107)\right) ]

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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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