SOLUTION: square root of -4 Absolute value of 5+4i over 7-5i

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Question 512605: square root of -4
Absolute value of 5+4i over 7-5i
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




First rationalize your denominator and then worry about the absolute value.

Multiply your fraction by the number 1 in the form of the conjugate of the denominator divided by itself. If you have a complex number , then is the conjugate. So you want to multiply your fraction by



Foil the numerator and recall that the product of conjugates is the difference of two squares. Don't forget that







Then recall that



You can do the rest of the arithmetic.

John

My calculator said it, I believe it, that settles it
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Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
square root of -4 = 2i
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Absolute value of 5+4i over 7-5i
|(5+4i)/(7-5i)|
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Multiply numerator and denominator by 7+5i to get
= |[(5+4i)(7+5i)]/(49+25)|
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= |(35+20+53i)/74|
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= |(55/74) + (53/74)i|
----
= sqrt[(55/74)^2 + (53/74)^2]
----
= sqrt(1.0654)
--------------
= 1.0322
============
Cheers,
Stan H.
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