Question

1.
For a non-zero complex number z, let arg(z) denote the
principal argument with -1 < arg(z) St. Then, which of
the following statement (s) is (are) FALSE?
TC
(A) arg(-1-i)
where i= -1
4'
(B) The function f:R (-4,1), defined by
f(t)= arg(-1+it) for all. tER, is continuous at all
points of R, where i = -1
(C) For any two non-zero complex numbers z, and zz,
31
arg
- arg(21) +arg(22)
22
is an integer multiple of 210
(D) For any three given distinct complex numbers 21, 22
and -z, the locus of the point z satisfying the condition
arg
(3-1)(32-23)
(2-2)(Z2-2)
= , lies on a straight line​

Answer 1

Answer:

1

For a non-zero complex number z, let arg(z) denote the

principal argument with -1 < arg(z) St. Then, which of

the following statement (s) is (are) FALSE?

TC

(A) arg(-1-i)

where i= -1

4'

(B) The function f:R (-4,1), defined by

f(t)= arg(-1+it) for all. tER, is continuous at all

points of R, where i = -1

(C) For any two non-zero complex numbers z, and zz,

31

arg

- arg(21) +arg(22)

22

is an integer multiple of 210

(D) For any three given distinct complex numbers 21, 22

and -z, the locus of the point z satisfying the condition

arg

(3-1)(32-23)

(2-2)(Z2-2)

= , lies on a straight line