Find the real and imaginary part of sin(4+3i)


by tatiana_eggs
Tags: imaginary, real, sin4
tatiana_eggs
tatiana_eggs is offline
#1
Sep18-10, 05:21 PM
P: 70
1. The problem statement, all variables and given/known data

Find the real and imaginary part of sin(4+3i)

2. Relevant equations

sinx = [tex]\frac{e^z - e^(-z)}{2i}[/tex]

cosx = [tex]\frac{e^z + e^(-z)}{2}[/tex]

sin(iy) = i[tex]\frac{e^y - e^(-y)}{2}[/tex]

cos(iy) = [tex]\frac{e^y + e^(-y)}{2}[/tex]

various trig identities

3. The attempt at a solution

So I used sin(x+y) trig identity and got
sin4*cos3i + sin3i*cos4

I turned them all into exponents using the appropriate equations stated in (2).

I got to a point where nothing is really calculable by hand/head. Is there an easier way to do this or does the calculator need to be used at a certain point to calculate the real part(terms grouped w/o i) and the imaginary part (terms grouped with i).

If so, then I guess I need help getting the terms grouped together to calculate the real and imaginary parts.

Where I am stuck is at:

[tex]\frac{e^{3+4i}+e^{-3+4i}-e^{3-4i}+e^{-3-4i}}{4i}[/tex] +
[tex]\frac{e^{3+4i}-e^{-3+4i}+e^{3-4i}-e^{-3-4i}}{4}[/tex]

(the two fractions should be added together)

Now what should I do with all these lovely exponents? Should I have even gone this route?
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
HallsofIvy
HallsofIvy is online now
#2
Sep18-10, 06:13 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,895
Quote Quote by tatiana_eggs View Post
1. The problem statement, all variables and given/known data

Find the real and imaginary part of sin(4+3i)

2. Relevant equations

sinx = [tex]\frac{e^z - e^(-z)}{2i}[/tex]

cosx = [tex]\frac{e^z + e^(-z)}{2}[/tex]

sin(iy) = i[tex]\frac{e^y - e^(-y)}{2}[/tex]

cos(iy) = [tex]\frac{e^y + e^(-y)}{2}[/tex]

various trig identities

3. The attempt at a solution

So I used sin(x+y) trig identity and got
sin4*cos3i + sin3i*cos4

I turned them all into exponents using the appropriate equations stated in (2).

I got to a point where nothing is really calculable by hand/head. Is there an easier way to do this or does the calculator need to be used at a certain point to calculate the real part(terms grouped w/o i) and the imaginary part (terms grouped with i).

If so, then I guess I need help getting the terms grouped together to calculate the real and imaginary parts.

Where I am stuck is at:

[tex]\frac{e^{3+4i}+e^{-3+4i}-e^{3-4i}+e^{-3-4i}}{4i}[/tex] +
[tex]\frac{e^{3+4i}-e^{-3+4i}+e^{3-4i}-e^{-3-4i}}{4}[/tex]

(the two fractions should be added together)

Now what should I do with all these lovely exponents? Should I have even gone this route?
Now use [itex]e^{3+ 4i}= e^3cos(4)+ i e^3sin(4)[/itex], etc.
tatiana_eggs
tatiana_eggs is offline
#3
Sep18-10, 06:46 PM
P: 70
That was just the hint I needed, Halls. Thanks! Finally got it.


Register to reply

Related Discussions
Wave Function: Real vs Imaginary Part Quantum Physics 0
HOW TO GET A REAL AND IMAGINARY PART FOR THIS e Calculus & Beyond Homework 0
Write as sum of real and imaginary part Calculus & Beyond Homework 3
identify the imaginary part Precalculus Mathematics Homework 4
Imaginary part in Ds General Physics 21