How Do You Convert sin^2(z) into x+iy Form?

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Homework Help Overview

The discussion revolves around converting the expression sin²(z) into the form x + iy, where z is expressed as x + iy. Participants are exploring the implications of this conversion and its relation to the arctan function.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to use trigonometric identities and exponential forms to express sin²(z), but encounters difficulties in isolating the imaginary unit i. They question whether sin only involves the imaginary part and express confusion regarding the behavior of sin(z) and cos(z) in this context. Other participants inquire about the nature of z, specifically whether it is real, and suggest expanding sin(x + iy) using a trigonometric identity.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations and approaches to the problem. Some guidance has been offered regarding the expansion of sin(x + iy), but no consensus has been reached on the original poster's approach or the nature of the variables involved.

Contextual Notes

The original poster expresses confusion about the relationship between the real and imaginary components in the context of trigonometric functions, indicating a need for clarification on these concepts.

jjangub
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Homework Statement


How do I change sin^2(z) to x+iy form? (z=x+iy)
I have to put this x and y to arctan(y/x)

Homework Equations


The Attempt at a Solution


I tried to use sin^2(z) = 1/2 -1/2(cos(2z)) or sin(z) = ((e^(iz) - e^(-iz))/2i)^2
but both ways I cannot take out i.
Or isn't the sin only takes the imagenary part? so there is no x and only y exists.
It brings us that artan(0) = 0?
I am confused about these cases like when there is sin(z) and cos(z)...
Thank you.
 
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z is real?
 
How would you expand Sin(x + i y)?
Using a trig identity.
 
jjangub said:

Homework Statement


How do I change sin^2(z) to x+iy form? (z=x+iy)
I have to put this x and y to arctan(y/x)

Homework Equations


The Attempt at a Solution


I tried to use sin^2(z) = 1/2 -1/2(cos(2z)) or sin(z) = ((e^(iz) - e^(-iz))/2i)^2
but both ways I cannot take out i.
Or isn't the sin only takes the imagenary part? so there is no x and only y exists.
It brings us that artan(0) = 0?
I am confused about these cases like when there is sin(z) and cos(z)...
Thank you.

that's not how it works
 

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