**TI86** Program file dated 06/23/04, 19:57 9 )ZTHEOR1C)'àTo7ZINITo4ZLoŽD0/D0/-i=1 IS AN IMAGINARY NUMBER.oŽD6/D0/-c=A+bi AND c=A-bi ARE COMPLEXoŽD12/D0/-CONJUGATES. THESE NUMBERS CAN BEoŽD18/D0/-CONVERTED TO POLAR FORM:x+iy=r*oŽD24/D0/-cos Á+ir sin Á=re^(iÁ), tan Á=y/xoŽD30/D0/-ADDITION: (A+bi)+(c+di)=(A+c)+(b+d)ioŽD36/D0/-SUBTRACTION:oŽD42/D0/-(A+bi)-(c+di)=(A-c)+(b-d)io4ZKoLD1/4MO/4T1/D2/4PR/3X/D4/4EX/3X/D5/4QU/3QoàT1oƒo4ZLoŽD0/D0/-MULTIPLY:oŽD6/D0/-(A+bi)(c+di)=Ac+Adi+bci-bdoŽD12/D0/-=(Ac-bd)+(Ad+bc)ioŽD18/D0/-PRODUCTS OF CONJUGATES:oŽD24/D0/-(A+bi)(A-bi)=A+boŽD30/D0/-TO DIVIDE MULTIPLY BY THE DENOMIN-oŽD36/D0/-ATOR'S CONJUGATE TO MAKE THEoŽD42/D0/-DENOMINATOR REAL: (A+bi)/(c+di)=o4ZKoLD1/4MO/4T2/D2/4PR/3T/D4/4EX/3X/D5/4QU/3QoàT2oƒo4ZLoŽD0/D0/-A+bi c-di Ac-Adi+bci-bdioŽD8/D0/-c+di c-di c+do–D0/D55/D11/D55o–D16/D55/D32/D55o–D38/D55/D92/D55oŽD3/D14/-*oŽD3/D35/-=oŽD3/D95/-=oŽD16/D0/-(Ac+bd)(bc-Ad)ioŽD24/D9/-c+do–D0/D39/D51/D39oŽD32/D0/-i=1, i^3=i*i=i, i^4=i*i=1oŽD40/D0/-i^5=i^4*i=i, i^6=i^5*i=1.o4ZKoLD1/4MO/4T3/D2/4PR/4T1/D4/4EX/3X/D5/4QU/3QoàT3oƒo4ZLoŽD0/D0/-(Ai)^n=iA^n, FOR n=1,5,9,13,...oŽD6/D20/-=A^n, FOR n=2,6,10,14,...oŽD12/D20/-=iA^n, FOR n=3,7,11,15,...oŽD18/D20/-=A^n, FOR n=4,8,12,16,...oŽD27/D0/-ie. 2=i2, 3=i3, 4=2i, 9=3ioŽD35/D0/-SEE 'IMAGINRY' PROG. FOR MOREo4ZKoLD2/4PR/4T2/D4/4EX/3X/D5/4QU/3QoàQnD1 3KoàXoßFo