document.write( "Question 238734: how do you find the square root of 25/3 using complex numbers? \n" ); document.write( "

Algebra.Com's Answer #175412 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
how do you find the square root of 25/3 using complex numbers?
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\n" ); document.write( "25/3 = 25/3 + 0i
\n" ); document.write( "---------------------
\n" ); document.write( "Trigonometric Form:
\n" ); document.write( "25/3+0i = (25/3)(cos(0)+isin(0))
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\n" ); document.write( "To take the square root:
\n" ); document.write( "(25/3)^(1/2) = (25/3)^1/2(cos[(0+2npi)/2] + isin([0+2npi)/2] for n = 0,1
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\n" ); document.write( "For n=0 you get:
\n" ); document.write( "(25/3)^(1/2)(cos(0) + isin(0) = sqrt(25/3) + 0i
\n" ); document.write( "------------------------------
\n" ); document.write( "For n=1 you get:
\n" ); document.write( "(25/3)^(1/2)(cos(pi)+isin(pi)) = -sqrt(25/3)+0i
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\n" ); document.write( "That is the complex number answer but I think you really
\n" ); document.write( "may have wanted the irrational number answer which is
\n" ); document.write( "as follows:
\n" ); document.write( "---
\n" ); document.write( "sqrt(25/3) = 5sqrt(1/3) = 5sqrt(3/9) = 5sqrt(3)/3
\n" ); document.write( "= (5/3)sqrt(3)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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