document.write( "Question 1131788: Write
\n" ); document.write( "z1 and z2 in polar form. (Express θ in radians. Let 0 ≤ θ < 2π.)
\n" ); document.write( "z1 = sqrt(3)+ i, z2 = 1 + sqrt(3i)\r
\n" ); document.write( "\n" ); document.write( "Find
\n" ); document.write( "z1z2
\n" ); document.write( "z1/z2
\n" ); document.write( "1/z1 \n" ); document.write( "
Algebra.Com's Answer #748549 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
Write
\n" ); document.write( "z1 and z2 in polar form. (Express θ in radians. Let 0 ≤ θ < 2π.)
\n" ); document.write( "z1 = sqrt(3)+ i,
\n" ); document.write( "Note:: z1 is in QI
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\n" ); document.write( "r1 = sqrt((sqrt(3))^2+1^2) = 2
\n" ); document.write( "theta = arctan(1/sqrt(3)) = pi/6
\n" ); document.write( "So r1 = 2cis(pi/6)
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\n" ); document.write( "z2 = 1 + sqrt(3)i
\n" ); document.write( "r2 = 2
\n" ); document.write( "theta = arctan(sqrt(3)) = pi/3
\n" ); document.write( "So r2 = 2cis(pi/3)
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\n" ); document.write( "Find
\n" ); document.write( "z1z2 = r1*r2*cis(pi/6+2pi/6) = 4*cis(pi/2)
\n" ); document.write( "z1/z2 = r1/r2*cis(pi/6-2pi/6) = cis(-pi/6)
\n" ); document.write( "1/z1 = (1+ 0i)/((sqrt(3)+i) = cis(0)/[2*cis(pi/6)] = (1/2)cis(-pi/6)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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