Question 150269
This problem is really difficult, I just can't seem to figure it out. Will someone PLEASE HELP ME!
If:
z = 6(cos 205 degrees + i sin 205 degrees) and w = 3(cos 85 degrees + i sin 85 degrees), which of the following is (z/w) in polar form?
1. 2(cos 290 degrees + i sin 290 degrees)
2. 0.5(cos(-120 degrees) + i sin (-120 degrees))
3. 18(cos 290 degrees + i sin 290 degrees)
4. 2(cos 120 degrees + i sin 120 degrees)

Thanks again for all of your help, I really appreciate it!
Natalie
<pre><font size = 4 color = "indigo"><b>
You just have to learn the rules for multiplying and dividing complex
numbers in trigonometric (or polar) form:

The rule for multiplying complex numbers in trig (polar) form is:

"multiply the r's and add the angles":

{{{  r[1]( cos(A[1])+i*sin(A[1]) )    r[2]( cos(B[2])+i*sin(B[2]) )   =
(r[1]r[2])( cos(A[1]+B[2])+i*sin(A[1]+B[2]) )  }}}

You don't need that one now but you will on other problems.

--------------------------------------

The rule for dividing complex numbers in polar form is similar:

"Divide the r's and subtract the angles":

{{{(  r[1]( cos(A[1])+i*sin(A[1]) )  )/(  r[2]( cos(B[2])+i*sin(B[2]) )  ) =
(r[1]/r[2])( cos(A[1]-B[2])+i*sin(A[1]-B[2]) )  }}}

z = 6(cos 205 degrees + i sin 205 degrees) 
w = 3(cos 85 degrees + i sin 85 degrees)

{{{z/w = (6 (cos(205)+i*sin(205) ))/(3(   cos(85)+i*sin(85)  ))=(6/3)(cos(205-85)+i*sin(205-85))=2(cos(120)+i*sin(120))}}}

Choice 4.

Edwin</pre>