Toughest Math P3 doubts! Here.

[Thought blocker]

(iii) arg(z) >= pi/3
I got this, but which z should i consider? 1+ isqrt(3) or 1 - isqrt(3) ??

 

[I Believe]

In q1: I've got (3x-1)In4 = In3 +xIn5 how do I solve it further?

and in q3: I get 1/8 [(π^2) -2] instead of 1/8 [(π^2) -4]

 

[Thought blocker]

View attachment 61275
(iii) arg(z) >= pi/3
I got this, but which z should i consider? 1+ isqrt(3) or 1 - isqrt(3) ??

I Believe help me with this till i help u with that

 

[Thought blocker]

View attachment 61276
In q1: I've got (3x-1)In4 = In3 +xIn5 how do I solve it further?

and in q3: I get 1/8 [(π^2) -2] instead of 1/8 [(π^2) -4]

For first question, first of all its ln not In
so , 3xln(4) - ln(4) = ln(3) + xln(5)
that will be, xln(64/5) = ln (12) thus x = 0.975

for third question what was ur integration?

 

[I Believe]

For first question, first of all its ln not In
so , 3xln(4) - ln(4) = ln(3) + xln(5)
that will be, xln(64/5) = ln (12) thus x = 0.975

for third question what was ur integration?

whoa!
I got the integral right, it was | (x^2 cos2x)/2 + xsinx/2 + cos2x/4 |

 

[Thought blocker]

whoa!
I got the integral right, it was | (x^2 cos2x)/2 + xsinx/2 + cos2x/4 |

m sure u made this whole integration to be zero when u substituted lower bound in this intgral, but that is 2/8 not 0
thus check ths, only this is the possible error u may have made.

 

[I Believe]

View attachment 61275
(iii) arg(z) >= pi/3
I got this, but which z should i consider? 1+ isqrt(3) or 1 - isqrt(3) ??

why will you consider 1 - i sqrt(3)
I don't know but I would draw a circle with center (0, -1) and a line that makes an angle of pi/3 with the positive x-axis, that seperates my circle in two segments, I would shade the lower segment...
but I'm not sure if I'm right, I'm having trouble in complex number's last parts as well

 

[Thought blocker]

why will you consider 1 - i sqrt(3)
I don't know but I would draw a circle with center (0, -1) and a line that makes an angle of pi/3 with the positive x-axis, that seperates my circle in two segments, I would shade the lower segment...
but I'm not sure if I'm right, I'm having trouble in complex number's last parts as well

z is also equal to 1 - isqrt(3) no?

 

[I Believe]

m sure u made this whole integration to be zero when u substituted lower bound in this intgral, but that is 2/8 not 0
thus check ths, only this is the possible error u may have made.

yes exactly thanks a lot
that's the mistake I was doing

 

[Thought blocker]

yes exactly thanks a lot
that's the mistake I was doing

TOLD YOU

 

[I Believe]

z is also equal to 1 - isqrt(3) no?

how?

 

[Thought blocker]

how?

if u is a root of z, u* will also be root of z, no?

 

[Thought blocker]

why will you consider 1 - i sqrt(3)
I don't know but I would draw a circle with center (0, -1) and a line that makes an angle of pi/3 with the positive x-axis, that seperates my circle in two segments, I would shade the lower segment...
but I'm not sure if I'm right, I'm having trouble in complex number's last parts as well

btw i would do the same.

 

[I Believe]

if u is a root of z, u* will also be root of z, no?

yes
I think so

 

[Thought blocker]

yes
I think so

so that is the confusion, which z should be taken into consideration. If u then why not u* ?

 

[I Believe]

so that is the confusion, which z should be taken into consideration. If u then why not u* ?

why not post on examsolutions

 

[Thought blocker]

why not post on examsolutions

Posted it on Further math page a few minutes ago.

 

[I Believe]

Posted it on Further math page a few minutes ago.

do tell me when you get an answer

 

[Thought blocker]

do tell me when you get an answer

Ya i got upload the slution here.

 

[Thought blocker]

View attachment 61275
(iii) arg(z) >= pi/3
I got this, but which z should i consider? 1+ isqrt(3) or 1 - isqrt(3) ??

I Believe Its same what we thought coz question asked about u, not u* Ali abdullah jan of furthermath page solved this on fb.