document.write( "Question 1138181: Let z1 = 1 - i√3 and z2 = -1 + i√3.
\n" ); document.write( "a) Express z1z2 in rectangular form.
\n" ); document.write( "b) Express z1, z2, and z1z2 in polar form.
\n" ); document.write( "c) Show that your answers to Part A and Part B are the same.
\n" ); document.write( "Make sure to show work.
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\n" ); document.write( "(a)

\n" ); document.write( "(b)

\n" ); document.write( "z1 = 1-1*sqrt(3):
\n" ); document.write( "\"r+=+sqrt%281%5E2%2B%28sqrt%283%29%29%5E2%29+=+sqrt%281%2B3%29+=+2\"
\n" ); document.write( "\"theta+=+arctan%28%28-1%2Asqrt%283%29%29%2F1%29+=+-pi%2F3\" (because z1 is in quadrant IV)
\n" ); document.write( "z1 = (2,-pi/3)

\n" ); document.write( "z2 = -1+i*sqrt(3):
\n" ); document.write( "\"r+=+sqrt%281%5E2%2B%28sqrt%283%29%29%5E2%29+=+sqrt%281%2B3%29+=+2\"
\n" ); document.write( "\"theta+=+arctan%28%28-1%2Asqrt%283%29%29%2F1%29+=+2pi%2F3\" (because z2 is in quadrant II)
\n" ); document.write( "z1 = (2,2pi/3)


\n" ); document.write( "z1*z2 = (2,-pi/3)*(2,2pi/3) = (4,pi/3)

\n" ); document.write( "c) (4,pi/3) =
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