Problem with solving a complex equation
$begingroup$
I'm having trouble solving this equation
$$Z^3=-4ibar Z$$
I need to find Z, I've tried multiplying the equation by Z but still couldnt solve it.
I'll be glad for help.
algebra-precalculus complex-numbers
edited Dec 28 '18 at 5:32
Eric Wofsey
190k14216347
asked Feb 26 '18 at 16:40
user534957user534957
275
$endgroup$
add a comment |
$begingroup$
I'm having trouble solving this equation
$$Z^3=-4ibar Z$$
I need to find Z, I've tried multiplying the equation by Z but still couldnt solve it.
I'll be glad for help.
algebra-precalculus complex-numbers
edited Dec 28 '18 at 5:32
Eric Wofsey
190k14216347
asked Feb 26 '18 at 16:40
user534957user534957
275
$endgroup$
add a comment |
$begingroup$
I'm having trouble solving this equation
$$Z^3=-4ibar Z$$
I need to find Z, I've tried multiplying the equation by Z but still couldnt solve it.
I'll be glad for help.
algebra-precalculus complex-numbers
edited Dec 28 '18 at 5:32
Eric Wofsey
190k14216347
asked Feb 26 '18 at 16:40
user534957user534957
275
$endgroup$
I'm having trouble solving this equation
$$Z^3=-4ibar Z$$
I need to find Z, I've tried multiplying the equation by Z but still couldnt solve it.
I'll be glad for help.
algebra-precalculus complex-numbers
algebra-precalculus complex-numbers
edited Dec 28 '18 at 5:32
Eric Wofsey
190k14216347
asked Feb 26 '18 at 16:40
user534957user534957
275
edited Dec 28 '18 at 5:32
Eric Wofsey
190k14216347
asked Feb 26 '18 at 16:40
user534957user534957
275
edited Dec 28 '18 at 5:32
Eric Wofsey
190k14216347
edited Dec 28 '18 at 5:32
Eric Wofsey
190k14216347
edited Dec 28 '18 at 5:32
Eric Wofsey
190k14216347
190k14216347
asked Feb 26 '18 at 16:40
user534957user534957
275
asked Feb 26 '18 at 16:40
user534957user534957
275
asked Feb 26 '18 at 16:40
user534957user534957
275
275
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Note that
$$Z^3=-4ibar Zimplies |Z^3|=4|Z|implies |Z|=0 quad lor quad |Z|=2$$
and for $|Z|=2$
$$Z^3=-4ibar Ziff Z^4=-4iZbar Z=-16i implies Z=2(-i)^frac14$$
answered Feb 26 '18 at 16:47
gimusigimusi
93k84594
$endgroup$
$begingroup$
Thank you for your comment!
$endgroup$
– user534957
Feb 26 '18 at 16:52
$begingroup$
Can i ask how did you calculate |Z^3|=4|Z|?
$endgroup$
– user534957
Feb 26 '18 at 16:53
$begingroup$
I get it. Very nice thank you so much!!
$endgroup$
– user534957
Feb 26 '18 at 16:55
$begingroup$
@user534957 I've taken the modulus both sides.
$endgroup$
– gimusi
Feb 26 '18 at 16:55
add a comment |
$begingroup$
I'd try taking the modulus of both sides: $|Z|^3=4|Z|$, from which $|Z| = 0$ or $2$.
For the case $|Z|=2$, we have $Z=2e^{itheta}$.
Can you progress from there?
answered Feb 26 '18 at 16:45
paw88789paw88789
29.4k12349
$endgroup$
add a comment |
$begingroup$
HINT.
$$Z = X + iY$$
$$bar Z = X - iY$$
Assuming the "bar" symbol denotes the complex conjugate.
If you multiply by $Z$ you get
$$(X + iY)^4 = 4i(X^2 + Y^2)$$
$$(X + iY)^4 = 4i (X + iY)(X - iY)$$
$$(X + iY)^3 = 4i(X - iY)$$
answered Feb 26 '18 at 16:43
Von NeumannVon Neumann
16.5k72545
$endgroup$
$begingroup$
How do I find z with this?
$endgroup$
– user534957
Feb 26 '18 at 16:46
$begingroup$
And thank you for your cimment i really appreciate it
$endgroup$
– user534957
Feb 26 '18 at 16:47
add a comment |
Your Answer
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Note that
$$Z^3=-4ibar Zimplies |Z^3|=4|Z|implies |Z|=0 quad lor quad |Z|=2$$
and for $|Z|=2$
$$Z^3=-4ibar Ziff Z^4=-4iZbar Z=-16i implies Z=2(-i)^frac14$$
answered Feb 26 '18 at 16:47
gimusigimusi
93k84594
$endgroup$
$begingroup$
Thank you for your comment!
$endgroup$
– user534957
Feb 26 '18 at 16:52
$begingroup$
Can i ask how did you calculate |Z^3|=4|Z|?
$endgroup$
– user534957
Feb 26 '18 at 16:53
$begingroup$
I get it. Very nice thank you so much!!
$endgroup$
– user534957
Feb 26 '18 at 16:55
$begingroup$
@user534957 I've taken the modulus both sides.
$endgroup$
– gimusi
Feb 26 '18 at 16:55
add a comment |
$begingroup$
Note that
$$Z^3=-4ibar Zimplies |Z^3|=4|Z|implies |Z|=0 quad lor quad |Z|=2$$
and for $|Z|=2$
$$Z^3=-4ibar Ziff Z^4=-4iZbar Z=-16i implies Z=2(-i)^frac14$$
answered Feb 26 '18 at 16:47
gimusigimusi
93k84594
$endgroup$
$begingroup$
Thank you for your comment!
$endgroup$
– user534957
Feb 26 '18 at 16:52
$begingroup$
Can i ask how did you calculate |Z^3|=4|Z|?
$endgroup$
– user534957
Feb 26 '18 at 16:53
$begingroup$
I get it. Very nice thank you so much!!
$endgroup$
– user534957
Feb 26 '18 at 16:55
$begingroup$
@user534957 I've taken the modulus both sides.
$endgroup$
– gimusi
Feb 26 '18 at 16:55
add a comment |
$begingroup$
Note that
$$Z^3=-4ibar Zimplies |Z^3|=4|Z|implies |Z|=0 quad lor quad |Z|=2$$
and for $|Z|=2$
$$Z^3=-4ibar Ziff Z^4=-4iZbar Z=-16i implies Z=2(-i)^frac14$$
answered Feb 26 '18 at 16:47
gimusigimusi
93k84594
$endgroup$
Note that
$$Z^3=-4ibar Zimplies |Z^3|=4|Z|implies |Z|=0 quad lor quad |Z|=2$$
and for $|Z|=2$
$$Z^3=-4ibar Ziff Z^4=-4iZbar Z=-16i implies Z=2(-i)^frac14$$
answered Feb 26 '18 at 16:47
gimusigimusi
93k84594
answered Feb 26 '18 at 16:47
gimusigimusi
93k84594
answered Feb 26 '18 at 16:47
gimusigimusi
93k84594
answered Feb 26 '18 at 16:47
gimusigimusi
93k84594
93k84594
$begingroup$
Thank you for your comment!
$endgroup$
– user534957
Feb 26 '18 at 16:52
$begingroup$
Can i ask how did you calculate |Z^3|=4|Z|?
$endgroup$
– user534957
Feb 26 '18 at 16:53
$begingroup$
I get it. Very nice thank you so much!!
$endgroup$
– user534957
Feb 26 '18 at 16:55
$begingroup$
@user534957 I've taken the modulus both sides.
$endgroup$
– gimusi
Feb 26 '18 at 16:55
add a comment |
$begingroup$
Thank you for your comment!
$endgroup$
– user534957
Feb 26 '18 at 16:52
$begingroup$
Can i ask how did you calculate |Z^3|=4|Z|?
$endgroup$
– user534957
Feb 26 '18 at 16:53
$begingroup$
I get it. Very nice thank you so much!!
$endgroup$
– user534957
Feb 26 '18 at 16:55
$begingroup$
@user534957 I've taken the modulus both sides.
$endgroup$
– gimusi
Feb 26 '18 at 16:55
$begingroup$
Thank you for your comment!
$endgroup$
– user534957
Feb 26 '18 at 16:52
$begingroup$
Thank you for your comment!
$endgroup$
– user534957
Feb 26 '18 at 16:52
$begingroup$
Can i ask how did you calculate |Z^3|=4|Z|?
$endgroup$
– user534957
Feb 26 '18 at 16:53
$begingroup$
Can i ask how did you calculate |Z^3|=4|Z|?
$endgroup$
– user534957
Feb 26 '18 at 16:53
$begingroup$
I get it. Very nice thank you so much!!
$endgroup$
– user534957
Feb 26 '18 at 16:55
$begingroup$
I get it. Very nice thank you so much!!
$endgroup$
– user534957
Feb 26 '18 at 16:55
$begingroup$
@user534957 I've taken the modulus both sides.
$endgroup$
– gimusi
Feb 26 '18 at 16:55
$begingroup$
@user534957 I've taken the modulus both sides.
$endgroup$
– gimusi
Feb 26 '18 at 16:55
add a comment |
$begingroup$
I'd try taking the modulus of both sides: $|Z|^3=4|Z|$, from which $|Z| = 0$ or $2$.
For the case $|Z|=2$, we have $Z=2e^{itheta}$.
Can you progress from there?
answered Feb 26 '18 at 16:45
paw88789paw88789
29.4k12349
$endgroup$
add a comment |
$begingroup$
I'd try taking the modulus of both sides: $|Z|^3=4|Z|$, from which $|Z| = 0$ or $2$.
For the case $|Z|=2$, we have $Z=2e^{itheta}$.
Can you progress from there?
answered Feb 26 '18 at 16:45
paw88789paw88789
29.4k12349
$endgroup$
add a comment |
$begingroup$
I'd try taking the modulus of both sides: $|Z|^3=4|Z|$, from which $|Z| = 0$ or $2$.
For the case $|Z|=2$, we have $Z=2e^{itheta}$.
Can you progress from there?
answered Feb 26 '18 at 16:45
paw88789paw88789
29.4k12349
$endgroup$
I'd try taking the modulus of both sides: $|Z|^3=4|Z|$, from which $|Z| = 0$ or $2$.
For the case $|Z|=2$, we have $Z=2e^{itheta}$.
Can you progress from there?
answered Feb 26 '18 at 16:45
paw88789paw88789
29.4k12349
answered Feb 26 '18 at 16:45
paw88789paw88789
29.4k12349
answered Feb 26 '18 at 16:45
paw88789paw88789
29.4k12349
answered Feb 26 '18 at 16:45
paw88789paw88789
29.4k12349
29.4k12349
add a comment |
add a comment |
$begingroup$
HINT.
$$Z = X + iY$$
$$bar Z = X - iY$$
Assuming the "bar" symbol denotes the complex conjugate.
If you multiply by $Z$ you get
$$(X + iY)^4 = 4i(X^2 + Y^2)$$
$$(X + iY)^4 = 4i (X + iY)(X - iY)$$
$$(X + iY)^3 = 4i(X - iY)$$
answered Feb 26 '18 at 16:43
Von NeumannVon Neumann
16.5k72545
$endgroup$
$begingroup$
How do I find z with this?
$endgroup$
– user534957
Feb 26 '18 at 16:46
$begingroup$
And thank you for your cimment i really appreciate it
$endgroup$
– user534957
Feb 26 '18 at 16:47
add a comment |
$begingroup$
HINT.
$$Z = X + iY$$
$$bar Z = X - iY$$
Assuming the "bar" symbol denotes the complex conjugate.
If you multiply by $Z$ you get
$$(X + iY)^4 = 4i(X^2 + Y^2)$$
$$(X + iY)^4 = 4i (X + iY)(X - iY)$$
$$(X + iY)^3 = 4i(X - iY)$$
answered Feb 26 '18 at 16:43
Von NeumannVon Neumann
16.5k72545
$endgroup$
$begingroup$
How do I find z with this?
$endgroup$
– user534957
Feb 26 '18 at 16:46
$begingroup$
And thank you for your cimment i really appreciate it
$endgroup$
– user534957
Feb 26 '18 at 16:47
add a comment |
$begingroup$
HINT.
$$Z = X + iY$$
$$bar Z = X - iY$$
Assuming the "bar" symbol denotes the complex conjugate.
If you multiply by $Z$ you get
$$(X + iY)^4 = 4i(X^2 + Y^2)$$
$$(X + iY)^4 = 4i (X + iY)(X - iY)$$
$$(X + iY)^3 = 4i(X - iY)$$
answered Feb 26 '18 at 16:43
Von NeumannVon Neumann
16.5k72545
$endgroup$
HINT.
$$Z = X + iY$$
$$bar Z = X - iY$$
Assuming the "bar" symbol denotes the complex conjugate.
If you multiply by $Z$ you get
$$(X + iY)^4 = 4i(X^2 + Y^2)$$
$$(X + iY)^4 = 4i (X + iY)(X - iY)$$
$$(X + iY)^3 = 4i(X - iY)$$
answered Feb 26 '18 at 16:43
Von NeumannVon Neumann
16.5k72545
answered Feb 26 '18 at 16:43
Von NeumannVon Neumann
16.5k72545
answered Feb 26 '18 at 16:43
Von NeumannVon Neumann
16.5k72545
answered Feb 26 '18 at 16:43
Von NeumannVon Neumann
16.5k72545
16.5k72545
$begingroup$
How do I find z with this?
$endgroup$
– user534957
Feb 26 '18 at 16:46
$begingroup$
And thank you for your cimment i really appreciate it
$endgroup$
– user534957
Feb 26 '18 at 16:47
add a comment |
$begingroup$
How do I find z with this?
$endgroup$
– user534957
Feb 26 '18 at 16:46
$begingroup$
And thank you for your cimment i really appreciate it
$endgroup$
– user534957
Feb 26 '18 at 16:47
$begingroup$
How do I find z with this?
$endgroup$
– user534957
Feb 26 '18 at 16:46
$begingroup$
How do I find z with this?
$endgroup$
– user534957
Feb 26 '18 at 16:46
$begingroup$
And thank you for your cimment i really appreciate it
$endgroup$
– user534957
Feb 26 '18 at 16:47
$begingroup$
And thank you for your cimment i really appreciate it
$endgroup$
– user534957
Feb 26 '18 at 16:47
add a comment |
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