Please Help with this complex number question!!!! (1 Viewer)

[umm what]

Can someone help with (iii) and (e)

THANKS A LOT!!!!

 

[bleakarcher]

iii) Let z=x+iy. Now, 0 is less than or equal to the real part of z which is less than or equal to 3. The Re(z)=Re(x+iy)=x. Therefore, it tells you that the region contains the set of all points with x coordinates lying between 0 and 3. But 1 is less than or equal to the imaginary part of z which is less than or equal to 2. The imaginary part of z Im(z)=Im(x+iy)=y. Therefore, the region is now the set of all points such that 0 is less than or equal to x which is less than or equal to 2 AND 1 is less than or equal to y which is less than or equal to 2 in the complex plane.

 

[someth1ng]

For (iii): It's pretty much 0<x<3 and 1<y<2
Show the double shaded region as the one that satisfies both.

 

[math man]

part (e) is wrong....geometrically speaking if
then that refers to the diagonals being equal when you do vector addition. Now there are only
two shapes that this occurs for, which is the square and rectangle, both of which have 90 degree
vertice angles. Now refers to the angle between
so the angle must be 90 and not 45

 

[someth1ng]

Now refers to the angle between
so the angle must be 90 and not 45

Why does it even need to have a fixed angle? Can't z2 be anything and still make a rectangle?

 

[math man]

its properties of geometry, if we are given the diagonals are equal, there are only two shapes that this occurs, due to pythegoras, which means the
vertice angles will be 90 degrees. I also confirmed this was wrong using algebra method (which is very long) and i ended up with tan inverse of undefined
number which means it has to be a multiple of 90, so it cant be pi/4, it can be a typo.

 

[umm what]

hey mate! thanks for the answer.... are you 100% sure about this?????

 

[umm what]

thanks brooo ))))

 

[someth1ng]

I just thought about it and "math man" is correct - the angle between z1 and z2 is indeed a right angle.

 

[math man]

and besides this question is in terry and cambridge too, its a typo in this paper, but the quickest and best method to do this question
is use properties of geometry and not to use algebra

 

[funnytomato]

I just thought about it and "math man" is correct - the angle between z1 and z2 is indeed a right angle.

+1

 

[funnytomato]

hopefully i still remember this

 

[funnytomato]

yeah, the picture worked

or i'm just imagining that

 

[umm what]

can u do (iii) and (d) plzzzz


THANK YOUUU SOO MUCHHH !!!