# How do you write the trigonometric form of #-4+2i#?

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To write the trigonometric form of the complex number (-4+2i), first, you need to find the magnitude (or modulus) and the argument (or angle) of the complex number.

The magnitude of a complex number (z = a + bi) is given by (|z| = \sqrt{a^2 + b^2}).

For (-4+2i), the magnitude is (|z| = \sqrt{(-4)^2 + 2^2} = \sqrt{16 + 4} = \sqrt{20}).

Next, you find the argument (or angle) using the formula (\theta = \arctan\left(\frac{b}{a}\right)).

For (-4+2i), the argument is (\theta = \arctan\left(\frac{2}{-4}\right) = \arctan\left(-\frac{1}{2}\right)).

Since (-4+2i) is in the second quadrant, you need to add (\pi) to the argument to get the principal argument.

Now, you can express the complex number (-4+2i) in trigonometric form as (z = \sqrt{20} \cdot \left(\cos\left(\arctan\left(-\frac{1}{2}\right) + \pi\right) + i \sin\left(\arctan\left(-\frac{1}{2}\right) + \pi\right)\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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