simple questions (1 Viewer)

[dawma88]

1) find x such that x < y and X^-1 < y^-1 ? ( y belongs to real numbers)

2) let z be a non-zero complex number. explain why o, z^-1 and congugate of z lie in a st line on the argand diagram

3) let z = x + iy where x,y belong to real a set of real numbers
write down lzl^2 and (REz)^2- i think lzl^2 = x^2 + y^2 and (REz)^2 = x^2

prove that lzl^2 >= REz- i think: x^2 + y^2 >= x^2 --> y^2 >= 0 thus since y is a positive the statement holds ??

for wat values of z does the equality hold ?

need help !

 

[Shady01]

what text book isthat out of? i cant read pc maths gotta see it in tha book

 

[Mountain.Dew]

1) find x such that x < y and X^-1 < y^-1 ? ( y belongs to real numbers)

2) let z be a non-zero complex number. explain why o, z^-1 and congugate of z lie in a st line on the argand diagram

3) let z = x + iy where x,y belong to real a set of real numbers
write down lzl^2 and (REz)^2- i think lzl^2 = x^2 + y^2 and (REz)^2 = x^2

prove that lzl^2 >= REz- i think: x^2 + y^2 >= x^2 --> y^2 >= 0 thus since y is a positive the statement holds ??

for wat values of z does the equality hold ?

need help !

for 2) ==> let z = rcis@.

now, z^-1 = 1/z = 1/r * (1/cos@ +isin@) = 1/r[cos@ - isin@] = [1/r][cos(-@) + isin(-@] = 1/rcis(-@)

so arg(z^-1) = -@

z conjugate = rcis(-@)

so arg(z conjugate) = -@

since arg(z^-1) = arg(z conjugate), and both complex numbers pass through O, then O, z^-1 and z conjugate lies on straight line, with angle (-@)

more to come...

 

[Mountain.Dew]

question:
3) let z = x + iy where x,y belong to real a set of real numbers
write down lzl^2 and (REz)^2- i think lzl^2 = x^2 + y^2 and (REz)^2 = x^2

first part is right lzl^2 = x^2 + y^2

2nd part...i dont think they would be so naive to do (REz)^2, rather, i think they want you to find Re(z^2). Re(z^2) = x^2 - y^2

and the 3rd part...its hard to prove lzl^2 >= REz, but its easier to prove lzl^2 >= (REz)^2

x^2 + y^2 >= x^2 >= x^2 - y^2, since x^2 and y^2 ARE ALWAYS POSITIVE

the equality holds when Im(z) = 0

 

[gman03]

1) find x such that x < y and X^-1 < y^-1 ? ( y belongs to real numbers)

Ans: True if x < 0 < y