H2MA Remedial _ Complex Numbers (RVHS)

Teacher’s copy 1 RVHS H2 Mathematics Remedial Programme Topic: Complex Numbers Basic Mastery Questions 1. MI Promo 9758/2020/PU2/P1/Q8(a) Given that 3ia=− and 5 2ib=+ , find the following complex numbers in the form ixy+ , (i) *ab , [2] (ii) * b a . [3] Answer: (i) 13 11i− , (ii) ( )1 17 i10 + 2. ASRJC Promo 9758/2020/Q8(a) It is given that two complex numbers z and w satisfy the following equations ( ) 2 i5 + 4i 1 z = 11 18i wz w += − − + Find z and w. [4] Click here or scan this to view video example on how to solve such question! 3. MI Promo 9758/2020/PU2/P1/Q8(b) (i) Express i 6eiz  =+ in the form of ier  . [3] (ii) Given that the complex number zw has modulus 12 and argument 2 3  , find the exact modulus and argument of complex number w. [3] Answer: (i) i 33e  , (ii) 4 3, 3r ==

Teacher’s copy 2 4. MI Promo 9758/2020/PU2/P2/Q2(i) Do not use a calculator in answering this question. The roots of the equation 2 8 6iz =− − are 1z and 2z . Find 1z and 2z in cartesian form, ixy+ , showing your working. [5] Click here or scan this to view video example on how to solve such question! Answer: 1 3i−+ , 1 3i− 5. VJC Prelim 9758/2021/01/Q8(a)(i) The complex number w is given by iewr = , where 0r  and 0 2  . Given that ( )1 i 3zw= −  , find z in terms of r and arg( )z in terms of  . [2] Click here or scan this to view video example on how to solve such question! Answers: 3  −+ , 2r

Teacher’s copy 3 Standard Questions 1. RI Promo 9758/2020/Q7(a) Do not use a calculator in answering this question. One root of the equation * 2i 6i,zz z a+ = + where a is real, is 3 7i.z=− Find the value of a and the other root. [4] Answer: a = 72, 3 9i+ 2. VJC Promo 9758/2020/Q10(a), (e) It is given that the complex number ( )3iw=−  − . Find the value of w . [1] Find the exact value of arg(w). [1] Without using a calculator, find the three smallest positive whole number values of n such that *nww is a real number. [3] Click here or scan this to view video example on how to solve such question! Answer: 2w = , 5arg 6w =− , 1, 7,13n=