document.write( "Question 967543: Multiply (sqrt(3) cis 15°)(2 cis 45°) and express the answer in rectangular coordinates. Give an exact answer. \n" ); document.write( "

Algebra.Com's Answer #591328 by stanbon(75887) $\"\"$ $\"About$

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Multiply (sqrt(3) cis 15°)(2 cis 45°) and express the answer in rectangular coordinates. Give an exact answer.
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\n" ); document.write( "(sqrt(3)cis(15))(2cis(45)) = 2sqrt(3)cis(60)
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\n" ); document.write( "Ans::
\n" ); document.write( "sqrt(x^2+y^2] = 2
\n" ); document.write( "x^2 + y^2 = 4
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\n" ); document.write( "60 = arctan(y/x)
\n" ); document.write( "y/x = tan(60) = sqrt(3)
\n" ); document.write( "x = y/sqrt(3)
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\n" ); document.write( "Substitute and solve for \"y\"::
\n" ); document.write( "[y^2/3 + y^2] = 4
\n" ); document.write( "(4/3)y^2 = 4
\n" ); document.write( "(1/3)y^2 = 1
\n" ); document.write( "y^2 = 3
\n" ); document.write( "y = sqrt(3)
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\n" ); document.write( "Solve for \"x\"::
\n" ); document.write( "x = y/sqrt(3) = sqrt(3)/sqrt(3) = 1
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\n" ); document.write( "Ans:: x+yi = 1+sqrt(3)i
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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