document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=63489>Question 63489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When we draw the complex number   i   as a point in the complex plane, its coordinates are <BR>\n" );
document.write( "a. (0, i )  <BR>\n" );
document.write( "b. (1,0)  <BR>\n" );
document.write( "c. (0,1)  <BR>\n" );
document.write( "d. The number  i  cannot be drawn as a point in the complex plane  \r<BR>\n" );
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document.write( "When we add the two complex numbers   a + bi  and  c + di   by representing them as points in the complex plane, then the sum is represented by  <BR>\n" );
document.write( "a. The corner of a rectangle whose other three corners are (0,0), (a,b), and   (c,d)  <BR>\n" );
document.write( "b. The corner of a triangle whose other two corners are (a,b) and (c,d)  <BR>\n" );
document.write( "c.  the corner of a parallelogram whose other three corners are (0,0),    (a,b),   and (c,d)  <BR>\n" );
document.write( "d. None of the above \r<BR>\n" );
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document.write( " Just like we do for the real numbers, we can draw a picture of the complex numbers simply by drawing a line.  <BR>\n" );
document.write( "a. True <BR>\n" );
document.write( "b.  False \r<BR>\n" );
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document.write( "The Division Algorithm for Polynomials and the Factor Theorem for Polynomials (which we proved when the polynomials have real number coefficients) are both TRUE even if the coefficients of the polynomials come from the complex numbers.  <BR>\n" );
document.write( "a True <BR>\n" );
document.write( "b. False \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #44170 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=44170\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When we draw the complex number i as a point in the complex plane, its coordinates are <BR>\n" );
document.write( "a. (0, i ) <BR>\n" );
document.write( "b. (1,0) <BR>\n" );
document.write( "c. (0,1) <BR>\n" );
document.write( "d. The number i cannot be drawn as a point in the complex plane <BR>\n" );
document.write( "Ans: (0,1) because the verticle axis becomes the imaginary part of the<BR>\n" );
document.write( "comples number 0+1i.<BR>\n" );
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document.write( "When we add the two complex numbers a + bi and c + di by representing them as points in the complex plane, then the sum is represented by <BR>\n" );
document.write( "a. The corner of a rectangle whose other three corners are (0,0), (a,b), and (c,d) <BR>\n" );
document.write( "b. The corner of a triangle whose other two corners are (a,b) and (c,d) <BR>\n" );
document.write( "c. the corner of a parallelogram whose other three corners are (0,0), (a,b), and (c,d) <BR>\n" );
document.write( "d. None of the above<BR>\n" );
document.write( "Ans: the corner of a parallelogram etc.......<BR>\n" );
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document.write( " <BR>\n" );
document.write( "Just like we do for the real numbers, we can draw a picture of the complex numbers simply by drawing a line. <BR>\n" );
document.write( "a. True <BR>\n" );
document.write( "b. False<BR>\n" );
document.write( "Ans: False ; you need a plane with a Real number line as horizontal axis<BR>\n" );
document.write( "and imaginary numbers as the vertical axis.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );