How do you simplify # (5i)/(2i)  (37i)/(23i)# and write in a+bi form?
Two distinct scenarios are possible:
The choice of approach is purely subjective and has little bearing on the outcome.
If it's okay with you, let me try the second strategy.
 Deduct the pair of terms.
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To simplify (\frac{5i}{2i}  \frac{37i}{23i}) and write it in (a+bi) form, follow these steps:
 Find a common denominator for both fractions.
 Combine the fractions.
 Write the result in (a+bi) form by separating the real and imaginary parts.
Solving step by step:

Find a common denominator: ((2i)(2+3i)) is a common denominator for both fractions.

Rewrite the fractions with the common denominator: (\frac{(5i)(2+3i)}{(2i)(2+3i)}  \frac{(37i)(2+i)}{(2i)(2+3i)})

Expand and simplify: (\frac{10 + 15i  2i  3i^2}{4 + 6i  2i  3i^2}  \frac{6 + 2i  3i  7i^2}{4 + 6i  2i  3i^2}) (\frac{10 + 13i  3(1)}{4 + 6i  2i  3(1)}  \frac{6  i  7(1)}{4 + 6i  2i  3(1)}) (\frac{10 + 13i + 3}{4 + 6i + 2  3}) and (\frac{6  i + 7}{4 + 6i + 2  3}) (\frac{13 + 13i}{3 + 6i}) and (\frac{13  i}{3 + 6i})

Combine the fractions: (\frac{(13 + 13i)  (13  i)}{3 + 6i}) (\frac{13 + 13i  13 + i}{3 + 6i}) (\frac{14i}{3 + 6i})

Multiply by the conjugate of the denominator to rationalize the expression: (\frac{14i(3  6i)}{(3 + 6i)(3  6i)}) (\frac{42i  84i^2}{9  18i + 18i  36i^2}) (\frac{42i + 84}{9 + 36}) (\frac{42i + 84}{45})

Separate into real and imaginary parts: (\frac{84}{45} + \frac{42}{45}i)

Simplify the fractions: ( \frac{28}{15} + \frac{14}{15}i)
So, (\frac{5i}{2i}  \frac{37i}{23i} = \frac{28}{15} + \frac{14}{15}i) in (a+bi) form.
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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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