How do you divide #( 2i 7) / ( 3 i 2 )# in trigonometric form?
Let us write the two complex numbers in polar coordinates and let them be
Their division leads us to
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To divide (2i  7) by (3i  2) in trigonometric form, follow these steps:

Multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of (3i  2) is (3i + 2). So, the expression becomes:
(2i  7) * (3i + 2) / (3i  2) * (3i + 2)

Perform the multiplication in the numerator and denominator:
Numerator: (2i * 3i) + (2 * 2i)  (7 * 3i)  (7 * 2) = 6i^2 + 4i  21i  14 = 6  17i
Denominator: (3i * 3i) + (3i * 2)  (2 * 3i)  (2 * 2) = 9i^2 + 6i  6i  4 = 9  4 = 13

Rewrite the division as a fraction:
(6  17i) / 13

Divide both the real and imaginary parts by the denominator (13):
Real part: 6 / 13 = 6/13 Imaginary part: 17i / 13 = 17i/13

Express the result in trigonometric form. In trigonometric form, a complex number (a + bi) is represented as (r(cosθ + isinθ)), where (r) is the modulus of the complex number and (θ) is the argument.
To find (r), the modulus: (r = \sqrt{a^2 + b^2})
Substitute (a = 6/13) and (b = 17/13): (r = \sqrt{(6/13)^2 + (17/13)^2} = \sqrt{(36/169) + (289/169)} = \sqrt{325/169})
To find (θ), the argument: (θ = \tan^{1}(\frac{b}{a}))
Substitute (a = 6/13) and (b = 17/13): (θ = \tan^{1}(\frac{17/13}{6/13}) = \tan^{1}(\frac{17}{6}))
So, the division of (2i  7) by (3i  2) in trigonometric form is ( \frac{\sqrt{325}}{13}(cos(\tan^{1}(\frac{17}{6})) + i sin(\tan^{1}(\frac{17}{6}))) ).
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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.
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