Understanding the Concept of Double Conjugate in Complex Functions

In summary, double conjugate confusion is a visual phenomenon caused by a misalignment or discrepancy between the eyes, resulting in distorted or overlapping images. It can be caused by factors such as eye misalignment, eye size or shape differences, or neurological disorders. It can be diagnosed through a comprehensive eye exam and can be treated with corrective lenses, eye exercises, or surgery. Long-term effects may include permanent vision problems and difficulties with depth perception and eye coordination.
  • #1
ognik
643
2
Hi, I am not sure what $ {f}^{*}({z}^{*}) $ means?
I think the '*'s cancel, ie $ {f}(z) = u(x,y) + iv(x,y), \: \therefore f({z}^{*}) = u(x,y) - iv(x,y), , \: \therefore {f}^{*}({z}^{*}) = u(x,y) + iv(x,y) $ ?
Thanks
 
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  • #2
Hi ognik,

If $z$ is represented by the point $(x,y) \in \Bbb R^2$, then $z^* = (x,-y)$. So given $f(z) = u(x,y) + iv(x,y)$, we have $f(z^*) = u(x,-y) + iv(x,-y)$ and hence $f^*(z^*) = u(x,-y)-iv(x,-y)$.
 
  • #3
Crystal! Thanks Euge.
 

Related to Understanding the Concept of Double Conjugate in Complex Functions

1. What is double conjugate confusion?

Double conjugate confusion is a phenomenon in which a person's brain processes visual information from both eyes, resulting in a distorted or overlapping image. This can occur when there is a misalignment or discrepancy between the eyes' focus or direction of movement.

2. What are the causes of double conjugate confusion?

Double conjugate confusion can be caused by a variety of factors, including a misalignment of the eyes (such as strabismus or lazy eye), a difference in the size or shape of the eyes, or a neurological disorder that affects eye movements.

3. How is double conjugate confusion diagnosed?

Double conjugate confusion can be diagnosed through a comprehensive eye exam, which may include tests to assess eye alignment, visual acuity, and eye movements. A doctor may also perform a cover test or use special instruments to measure the angle of eye deviation.

4. Can double conjugate confusion be treated?

Yes, double conjugate confusion can be treated. Depending on the underlying cause, treatment may include wearing corrective lenses, using eye exercises to improve eye alignment, or surgery to correct any structural issues with the eyes. In some cases, vision therapy may also be recommended.

5. What are the long-term effects of double conjugate confusion?

The long-term effects of double conjugate confusion can vary depending on the severity and underlying cause. In some cases, it may lead to permanent vision problems, such as amblyopia (lazy eye) or binocular vision dysfunction. It may also impact a person's depth perception and ability to perform certain tasks that require good eye coordination.

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