Question 150314
Please help me with this!
If:
z=4(cos 50 degrees + i sin 50 degrees) and w=2(cos 340 degrees + i sin 340 degrees), find z/w in polar form.
The choices that are given are:
1. 8(cos 390 degrees + i sin 390 degrees)
2. 2[cos (-290 degrees) + i sin (-290 degrees)]
3. 2(cos 290 degrees + i sin 290 degrees)
4. 2(cos 110 degrees + i sin 110 degrees)
Thanks, Tami

<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 = 4(cos(50) + i sin(50))}}} 
{{{w = 2(cos(340) + i sin(340))}}}

{{{z/w = (4 (cos(50)+i*sin(50) ))/(2(   cos(340)+i*sin(340)  ))=(4/2)(cos(50-340)+i*sin(50-340))=2(cos(-290)+i*sin(-290))}}}

Choice 2.

Edwin</pre>