Questions on Algebra: Complex Numbers answered by real tutors!

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Start with the given expression.


Multiply both numerator and denominator by the complex conjugate of


Combine the fractions


Foil the denominator to get


Distribute


So


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Start with the given expression.


Flip the fraction to make the exponent positive.

Now let's find evaluate :

First take the exponent 35 and divide by 4.
When it leaves a remainder of 0, the answer is .
When it leaves a remainder of 1, the answer is .
When it leaves a remainder of 2, the answer is .
When it leaves a remainder of 3, the answer is .


Since leaves a remainder of 3, this means the answer is .


So


So this means that







Start with the given expression.



Multiply both numerator and denominator by "i"


Combine the fractions.


Multiply and to get


Replace with . Remember


Multiply


Simplify


So

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I'm not quite sure how to simplify the expression 4 over 2+5i (4/2+5i) and I'm not quite sure what i to the -35th power means.
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4/(2+5i)
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Multiply numerator and denominator by (2-5i) to get:
[4(2-5i)]/[4+25]
= (8-20i)/29
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i^(-35)
Applying the -1 exponent you get:
(i^3)^35
Applying the 35 exponent you get:
= i^105
= i^(104+1)
= i^(104) * i^1
= 1 * i^1
= i
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Cheers,
Stan H.

You can put this solution on YOUR website!
i^(-35)
1/i^35
1/( i * i^34 ) ~ you want an even power
1/( i * (i^2)^17 ) ~ now, you want an exponent of 2
1/( i * (-1)^17 ) ~ i^2 = -1
-1 / i ~ (-1)^17 = -1
..
4 / (2 + 5i)
4(2 - 5i) / (2 + 5i)(2 - 5i) ~ multiply the num. and dem. by the conjugate