COmplex Numbers (2 Viewers)

[EvoRevolution]

Given that z = x + iy, where x,y are real, find an expression for arg(z) if:

(a) x>0, y=0
(b) x<0,y=0
(c)x=0,y>0
(d) x>0,y>0
(f)x<0,y<0

 

[vds700]

Given that z = x + iy, where x,y are real, find an expression for arg(z) if:

(a) x>0, y=0
(b) x<0,y=0
(c)x=0,y>0
(d) x>0,y>0
(f)x<0,y<0

this is pretty simple, just sketch z on an argand diagram for each case, use trig if necessary

a)z lies on the positive half the the x-axis(real), so arg z = 0

b) z is on the negative half of the x-axis, therefore arg z = pi

you should be able to work out the rest

 

[Aerath]

Hmmm, isn't b) argz = pi

And just for my sake, are these the rest of the answers?
c) pi/2
d) 0 < argz < pi/2
e) pi < argz <3pi/4

 

[vds700]

Hmmm, isn't b) argz = pi

And just for my sake, are these the rest of the answers?
c) pi/2
d) 0 < argz < pi/2
e) pi < argz <3pi/4

fuck you're right....my bad

and i though d and e were:

d) tan^-1(y/x)
e)tan^-1(y/x) - pi

 

[lilainjel]

About answers for (d) and (e), don't they have to be given so that angle is in the domain 0 < argz < pi or -pi/2 < argz < 0 ??

So I thought answers would be
(d) 0 < argz < pi/2

(e) -pi < argz < -pi/2

 

[independantz]

Given that z = x + iy, where x,y are real, find an expression for arg(z) if:

(a) x>0, y=0
(b) x<0,y=0
(c)x=0,y>0
(d) x>0,y>0
(f)x<0,y<0

a) arg(z)=0
b) arg(z)=-pi
c) arg(z)=pi/2
d) 0 < arg(z) < pi/2
e) -pi < arg(z) < -pi/2

 

[vds700]

About answers for (d) and (e), don't they have to be given so that angle is in the domain 0 < argz < pi or -pi/2 < argz < 0 ??

So I thought answers would be
(d) 0 < argz < pi/2

(e) -pi < argz < -pi/2

but the question said, find an expression for arg z, you're just giving the range of arg z.

Really sorry if im wrong though....