document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252737>Question 252737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 9) the expression i to the 25 power is eqivalen to?<BR>\n" );
document.write( "a) -i<BR>\n" );
document.write( "b)1<BR>\n" );
document.write( "c)i<BR>\n" );
document.write( "d)-1\r<BR>\n" );
document.write( "\n" );
document.write( "10) What does the expression i to 100th power + i to the 101 power + i to the 102 power equal?<BR>\n" );
document.write( "a) 1<BR>\n" );
document.write( "b)i<BR>\n" );
document.write( "c)-i<BR>\n" );
document.write( "d)-1\r<BR>\n" );
document.write( "\n" );
document.write( "11) What is the sum of 5-3i and the conjugate of 3+2i?<BR>\n" );
document.write( "12) The expression 3i(2isquared-5i) is eqivalent to?<BR>\n" );
document.write( "a)15-5i<BR>\n" );
document.write( "b)-15-5i<BR>\n" );
document.write( "c)8+5i<BR>\n" );
document.write( "d)2-5i\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184803 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=184803\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 9) the expression i to the 25 power is eqivalen to?<BR>\n" );
document.write( "a) -i<BR>\n" );
document.write( "b)1<BR>\n" );
document.write( "c)i<BR>\n" );
document.write( "d)-1<BR>\n" );
document.write( "The powers of i are cyclic mod 4, meaning there are 4 possibilities.<BR>\n" );
document.write( "exp...value<BR>\n" );
document.write( "1....i<BR>\n" );
document.write( "2....-1<BR>\n" );
document.write( "3....-i<BR>\n" );
document.write( "4....+1<BR>\n" );
document.write( "Then it repeats.  For the 25th power, divide 25 by 4 and get the remainder. That's 25 mod 4, or in Excel, mod(25,4) and the remainder is 1.<BR>\n" );
document.write( "i^1 = i<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "10) What does the expression i to 100th power + i to the 101 power + i to the 102 power equal?<BR>\n" );
document.write( "a) 1<BR>\n" );
document.write( "b)i<BR>\n" );
document.write( "c)-i<BR>\n" );
document.write( "d)-1<BR>\n" );
document.write( "i^100 = 1<BR>\n" );
document.write( "1^101 = i<BR>\n" );
document.write( "i^102 = -1<BR>\n" );
document.write( "---------- Add<BR>\n" );
document.write( "= i<BR>\n" );
document.write( "---<BR>\n" );
document.write( "11) What is the sum of 5-3i and the conjugate of 3+2i?<BR>\n" );
document.write( "The conjugate of 3+2i is 3-2i<BR>\n" );
document.write( "5-3i<BR>\n" );
document.write( "3-2i<BR>\n" );
document.write( "----- Add<BR>\n" );
document.write( "8-5i<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "12) The expression 3i(2isquared-5i) is eqivalent to?<BR>\n" );
document.write( "a)15-5i<BR>\n" );
document.write( "b)-15-5i<BR>\n" );
document.write( "c)8+5i<BR>\n" );
document.write( "d)2-5i <BR>\n" );
document.write( "3i*(2i^2 - 5i)<BR>\n" );
document.write( "= 3i*(-2 - 5i)<BR>\n" );
document.write( "= -6i - 15i^2<BR>\n" );
document.write( "= -6i - 15*(-1)<BR>\n" );
document.write( "= 15 - 6i<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );