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(chatquestion)...Maths lecture.pdf 2. Show that ) (z+1)? = z +2z+1 b) Im(iz) = Re(z) a) Re(z) = - Im(z) 3. Do the following operations and simplify your answer. 1+21 2-1 a) 3-41 5/ C) (1-0* ) 1-0 (2-0 (3-) 51 4. Locate the complex numbers z1+Zz and z-Z2, as vectors where b) z = (-13, 1) . z, = (3,0) a) z, = 21, z, = c) z, = (-3, 1), z, = (1, 4) d) z = a+ ib, z, - a- ib 5. Sketch the following set of points determined by the condition given below: a) | z-1+/-1 b) |z+153 c) |z-4/2 4 61 6. Using properties of conjugate and modulus, show that b) iz =-1Z c) (2+0 = 3- 4/ a) z+3/ = z-3/ 7. Show that (-1+1)' = 8(-1-). 8. Using mathematical induction, show that (whenn - 2, 3, ...) a) z, + z, + ..+ z, = 4 + z, +.+ z, b) z,2, ..Z, = z, Z, ** Z, Show that the equation z- z, Fr which is a circle of radius r centered at z, can be written 9. as | 리-2Re(zz)+|2,1-r. 2.2.6 Argument (Amplitude) of a complex number Definition 2.15 Argument of a complex number z - X+ly is the angle formed by the complex number z - X+ly with the positive x-axis. The argument of a complex number z - x+iy is deonted by argz and is given by arg(z) - tan The particular argument of z that lies in the range -<0Sn is called the principal argument of z and is dented by Argz. Notes:) Argze (-n,7} i) If Os ArgzSA, move counterclock wise direction if not move the other direction 61 Example 2.50: Find the principal argument of the following complex numbers: !!!

asked Feb 17, 2020 by balaji.thirumalai
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