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

Question 512605: square root of -4
Absolute value of 5+4i over 7-5i
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) (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

Answer by stanbon(75887) (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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