document.write( "Question 867773: Please help. I do not understand\r
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\n" ); document.write( "1.) 3(cos*pi/3 + sin*pi/3)
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\n" ); document.write( "write the complex number in polar form. Express the argument theta in degrees, with 0 less than or equal to theta less than or equal to 360 degrees.
\n" ); document.write( "2.) 3 sqrt 3 - 3i
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\n" ); document.write( "convert the polar equation to rectangular form.
\n" ); document.write( "3.) r = 5 \n" ); document.write( "
Algebra.Com's Answer #523221 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Write the complex number in rectangular form.
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document.write( "1.) \"3%28cos%28pi%2F3%29+%2B+i%2Asin%28pi%2F3%29%29\"\r\n" );
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document.write( "Just evaluate it:\r\n" );
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document.write( "    \"3%281%2F2%2Bi%2A+expr%28sqrt%283%29%2F2%29%29+\"\r\n" );
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document.write( "    \"3%2F2%2Bexpr%283sqrt%283%29%2F2%29i+\"\r\n" );
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write the complex number in polar form. Express the argument theta in degrees, with 0 less than or equal to theta less than or equal to 360 degrees.
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document.write( "3√3 - 3i = x + iy,\r\n" );
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document.write( "where  P(x,y) =  P(3√3,-3),\r\n" );
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document.write( "Plot the point P(x,y) = P(3√3,-3),\r\n" );
document.write( "draw a line from P to the origin, \r\n" );
document.write( "and another line from P perpendicular to the x-axis.  \r\n" );
document.write( "Label the sides of the resulting right triangle x,y, and r,\r\n" );
document.write( "Label the counter-clockwise angle q.\r\n" );
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document.write( "Since the point P is P(x,y) =  P(3√3,-3), x = 3√3 and y = -3.\r\n" );
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document.write( "We calculate r:\r\n" );
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document.write( "r² = x² + y²\r\n" );
document.write( "r² = (3√3)² + (-3)².\r\n" );
document.write( "r² = 9(3) + 9\r\n" );
document.write( "r² = 27 + 9\r\n" );
document.write( "r² = 36\r\n" );
document.write( " r = √36\r\n" );
document.write( " r = 6\r\n" );
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document.write( "\"sin%28theta%29=y%2Fr=%28-3%29%2F6=-1%2F2\"\r\n" );
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document.write( "Therefore q = 330°,\r\n" );
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document.write( "since it is in Q4, with a reference angle of 30°.\r\n" );
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document.write( "    Use \"x%2Fr=cos%28theta%29\" and \"y%2Fr=sin%28theta%29\".\r\n" );
document.write( "Solve them for x and y\r\n" );
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document.write( "    \"x=r%2Acos%28theta%29\" and \"y=r%2Asin%28theta%29\"\r\n" );
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document.write( "    x = 6*cos(330°) and y = 6*sin(330°)\r\n" );
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document.write( "So\r\n" );
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document.write( "3√3 - 3i = x + iy =  6*cos(330°) + i*6sin(330°) = 6(cos(330° + isin(330°)  \r\n" );
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document.write( "convert the polar equation to rectangular form.\r\n" );
document.write( "3.) r = 5\r\n" );
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document.write( "That is a circle at the origin (pole) with a radius of 5.\r\n" );
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document.write( "r² = x² + y²\r\n" );
document.write( "5² = x² + y²\r\n" );
document.write( "x² + y² = 25\r\n" );
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document.write( "Edwin
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