Q)
(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-)
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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
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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
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Example 2.50: Find the principal argument of the following complex numbers:
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