# How do you divide #10/(10+5i)#?

you gotta multiply the denominator by its conjugate to make it real...and of course do the same to the denominator, with the result that the numerator will have the real and imaginary parts

BACKGROUND:

so here we have

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To divide 10 by (10 + 5i), you first need to rationalize the denominator. To do this, multiply both the numerator and the denominator by the conjugate of the denominator, which is 10 - 5i. This will eliminate the imaginary component from the denominator.

10/(10 + 5i) * (10 - 5i) / (10 - 5i) = (10 * (10 - 5i)) / (10 * (10 - 5i) + 5i * (10 - 5i))

Now, multiply out the numerators and denominators:

Numerator: 10 * (10 - 5i) = 100 - 50i Denominator: (10 * (10 - 5i)) + (5i * (10 - 5i)) = 100 - 50i + 50i + 25 = 125

So, the final result is:

(100 - 50i) / 125

Which simplifies to:

(20 - 10i) / 25

Further simplification yields:

20/25 - (10i)/25

So, the division of 10 by (10 + 5i) is:

20/25 - (10/25)i

Which can be simplified to:

4/5 - (2/5)i

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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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