Equation

Art of Problem Solving

AoPS Online

High School Math Grades 9-12, Ages 13-18

Grades 9-12, Ages 13-18

3 M G

BBookmark VNew Topic kLocked

High School Math Grades 9-12, Ages 13-18

Grades 9-12, Ages 13-18

3 M G

BBookmark VNew Topic kLocked

B

No tags match your search

M

Equation

G H J

Reveal topic tags

L

G H BBookmark kLocked kLocked NReply

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

18 posts

#1 h Mar 15, 2016, 9:04 PM • 2 Y

Y by Adventure10, Mango247

HI
Solve this equation :

Attachments:

This post has been edited 1 time. Last edited by algharib, Mar 15, 2016, 9:08 PM
Reason: equatin

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

algebra_star1234

2467 posts

algebra_star1234

#2 h Mar 15, 2016, 9:08 PM • 2 Y

Y by Adventure10, Mango247

algharib wrote:

HI
Solve this equation :
$z^{2}+2i\overline{z}=0$
$z\in \mathbb{C}$

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

2659 posts

#3 h Mar 15, 2016, 9:15 PM • 2 Y

Y by Adventure10, Mango247

Set $z=a+ib$ then complex quadratic bash? Also note that $0$ works.
$a^2-b^2+2abi+2i(a-ib)=0$ , then simplify, and equate real and imaginary parts.

This post has been edited 1 time. Last edited by mathguy5041, Mar 15, 2016, 9:17 PM

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

258 posts

#4 h Mar 15, 2016, 9:19 PM • 1 Y

Y by Adventure10

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

1675 posts

#5 h Mar 15, 2016, 9:47 PM • 2 Y

Y by Adventure10, Mango247

rlzhang wrote:

No, $z^2$ isn't necessarily $0$ and $2i\overline{z}$ is not necessarily $0$

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

2659 posts

#6 h Mar 15, 2016, 10:04 PM • 3 Y

Y by speck, Adventure10, Mango247

mathguy5041 wrote:

Set $z=a+ib$ then complex quadratic bash? Also note that $0$ works.
$a^2-b^2+2abi+2i(a-ib)=0$ , then simplify, and equate real and imaginary parts.

Z K Y

The post below has been deleted. Click to close.

This post has been deleted. Click here to see post.

7054 posts

#7 h Apr 18, 2016, 1:59 PM • 2 Y

Y by Adventure10, Mango247

See PP5 from here

This post has been edited 1 time. Last edited by Virgil Nicula, Apr 18, 2016, 2:00 PM

Z K Y

N Quick Reply

G

H

=

© 2025 AoPS Incorporated

a