How do I simplify $|z^4 + iz + 1|$
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0
down vote
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In general, I would like to know which is the best approach in solving this deg $4$ complex polynomial.
This seems too complex and I am missing something fundamental?
polynomials complex-numbers
asked Nov 13 at 10:41
2deviate
11
add a comment |
up vote
0
down vote
favorite
In general, I would like to know which is the best approach in solving this deg $4$ complex polynomial.
This seems too complex and I am missing something fundamental?
polynomials complex-numbers
asked Nov 13 at 10:41
2deviate
11
ah much appreciated. thanks.
– 2deviate
Nov 13 at 13:04
I have tried to delete this but to no avail. Please ignore. Thanks.
– 2deviate
Nov 13 at 13:47
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
In general, I would like to know which is the best approach in solving this deg $4$ complex polynomial.
This seems too complex and I am missing something fundamental?
polynomials complex-numbers
asked Nov 13 at 10:41
2deviate
11
In general, I would like to know which is the best approach in solving this deg $4$ complex polynomial.
This seems too complex and I am missing something fundamental?
polynomials complex-numbers
polynomials complex-numbers
asked Nov 13 at 10:41
2deviate
11
asked Nov 13 at 10:41
2deviate
11
edited Nov 13 at 13:45
asked Nov 13 at 10:41
2deviate
11
asked Nov 13 at 10:41
2deviate
11
asked Nov 13 at 10:41
2deviate
11
11
ah much appreciated. thanks.
– 2deviate
Nov 13 at 13:04
I have tried to delete this but to no avail. Please ignore. Thanks.
– 2deviate
Nov 13 at 13:47
add a comment |
ah much appreciated. thanks.
– 2deviate
Nov 13 at 13:04
I have tried to delete this but to no avail. Please ignore. Thanks.
– 2deviate
Nov 13 at 13:47
ah much appreciated. thanks.
– 2deviate
Nov 13 at 13:04
ah much appreciated. thanks.
– 2deviate
Nov 13 at 13:04
I have tried to delete this but to no avail. Please ignore. Thanks.
– 2deviate
Nov 13 at 13:47
I have tried to delete this but to no avail. Please ignore. Thanks.
– 2deviate
Nov 13 at 13:47
add a comment |
1 Answer
1
active
oldest
votes
up vote
6
down vote
$$|z^3+(-iz)+1|le|z^3|+|-iz|+|1|=|z|^3+|-i||z|+1=3^3+1cdot3+1$$
See : Useful Inequalities Among Complex Numbers
answered Nov 13 at 10:43
lab bhattacharjee
220k15154271
This is basically an application of triangle inequality twice, isn't it? Together with properties of the norm of powers of complex numbers.
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:56
$|a+b+c| leq | a+b| + |c| leq |a|+ |b| + |c| $ and $|z^3|=|z|^3$
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:58
Yes I see that now. Much appreciated. Thanks.
– 2deviate
Nov 13 at 13:05
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
6
down vote
$$|z^3+(-iz)+1|le|z^3|+|-iz|+|1|=|z|^3+|-i||z|+1=3^3+1cdot3+1$$
See : Useful Inequalities Among Complex Numbers
answered Nov 13 at 10:43
lab bhattacharjee
220k15154271
This is basically an application of triangle inequality twice, isn't it? Together with properties of the norm of powers of complex numbers.
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:56
$|a+b+c| leq | a+b| + |c| leq |a|+ |b| + |c| $ and $|z^3|=|z|^3$
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:58
Yes I see that now. Much appreciated. Thanks.
– 2deviate
Nov 13 at 13:05
add a comment |
up vote
6
down vote
$$|z^3+(-iz)+1|le|z^3|+|-iz|+|1|=|z|^3+|-i||z|+1=3^3+1cdot3+1$$
See : Useful Inequalities Among Complex Numbers
answered Nov 13 at 10:43
lab bhattacharjee
220k15154271
This is basically an application of triangle inequality twice, isn't it? Together with properties of the norm of powers of complex numbers.
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:56
$|a+b+c| leq | a+b| + |c| leq |a|+ |b| + |c| $ and $|z^3|=|z|^3$
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:58
Yes I see that now. Much appreciated. Thanks.
– 2deviate
Nov 13 at 13:05
add a comment |
up vote
6
down vote
up vote
6
down vote
$$|z^3+(-iz)+1|le|z^3|+|-iz|+|1|=|z|^3+|-i||z|+1=3^3+1cdot3+1$$
See : Useful Inequalities Among Complex Numbers
answered Nov 13 at 10:43
lab bhattacharjee
220k15154271
$$|z^3+(-iz)+1|le|z^3|+|-iz|+|1|=|z|^3+|-i||z|+1=3^3+1cdot3+1$$
See : Useful Inequalities Among Complex Numbers
answered Nov 13 at 10:43
lab bhattacharjee
220k15154271
edited Nov 13 at 11:36
answered Nov 13 at 10:43
lab bhattacharjee
220k15154271
answered Nov 13 at 10:43
lab bhattacharjee
220k15154271
answered Nov 13 at 10:43
lab bhattacharjee
220k15154271
220k15154271
This is basically an application of triangle inequality twice, isn't it? Together with properties of the norm of powers of complex numbers.
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:56
$|a+b+c| leq | a+b| + |c| leq |a|+ |b| + |c| $ and $|z^3|=|z|^3$
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:58
Yes I see that now. Much appreciated. Thanks.
– 2deviate
Nov 13 at 13:05
add a comment |
This is basically an application of triangle inequality twice, isn't it? Together with properties of the norm of powers of complex numbers.
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:56
$|a+b+c| leq | a+b| + |c| leq |a|+ |b| + |c| $ and $|z^3|=|z|^3$
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:58
Yes I see that now. Much appreciated. Thanks.
– 2deviate
Nov 13 at 13:05
This is basically an application of triangle inequality twice, isn't it? Together with properties of the norm of powers of complex numbers.
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:56
This is basically an application of triangle inequality twice, isn't it? Together with properties of the norm of powers of complex numbers.
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:56
$|a+b+c| leq | a+b| + |c| leq |a|+ |b| + |c| $ and $|z^3|=|z|^3$
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:58
$|a+b+c| leq | a+b| + |c| leq |a|+ |b| + |c| $ and $|z^3|=|z|^3$
– WesleyGroupshaveFeelingsToo
Nov 13 at 10:58
Yes I see that now. Much appreciated. Thanks.
– 2deviate
Nov 13 at 13:05
Yes I see that now. Much appreciated. Thanks.
– 2deviate
Nov 13 at 13:05
add a comment |
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ah much appreciated. thanks.
– 2deviate
Nov 13 at 13:04
I have tried to delete this but to no avail. Please ignore. Thanks.
– 2deviate
Nov 13 at 13:47