Complex Number : 5th

© 2007 -2010 tutorco.com 1 Q1. Express the following in standard form of complex number (a + ib) : a) (2+3i) /(4+5i) b) (1 +i )3 /(1 – i3 ) Q2. Find the following: a) x4 + 9x3 + 35 x2 – x + 4 ; x = -5 + 2-4 Pre/TOPIC: COMPLEX NUMBER Cal © 2007 -2010 tutorco.com 2 b) x3 + 7 x2 – x + 16 ; x = 1 + 2i c) 2x3 + 2 x2 – 7x + 72 ; x = (3 -5i) /2 © 2007 -2010 tutorco.com 3 d) x4 + 4x3 + 6x2 + 4x + 9 ; x = -1 + 2 i Q3. Prove that: x4 + 4 = (x + 1 +i)(x + 1 –i)(x – 1 +i)(x – 1 –i) © 2007 -2010 tutorco.com 4 Q4. Find least positive value of n, if [(1+i) /(1 – i)]n = 1 Q5. If z = 2+ 3i then show that z2 + 4z + 13 = 0 and also find the value of: 4z3 -3z2 +169 © 2007 -2010 tutorco.com 5 Q6. Find the solutions of : | 1 – i | x = 2x Q7.If, Find: © 2007 -2010 tutorco.com 6 Q8. Its given: . ; Find: a) b)