You can
put this solution on YOUR website!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
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":
+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]) )](/cgi-bin/plot-formula.mpl?expression=++r%5B1%5D%28+cos%28A%5B1%5D%29%2Bi%2Asin%28A%5B1%5D%29+%29++++r%5B2%5D%28+cos%28B%5B2%5D%29%2Bi%2Asin%28B%5B2%5D%29+%29+++=%0D%0A%28r%5B1%5Dr%5B2%5D%29%28+cos%28A%5B1%5D%2BB%5B2%5D%29%2Bi%2Asin%28A%5B1%5D%2BB%5B2%5D%29+%29++&x=0003)
You don't need that one now but you will on other problems.
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The rule for dividing complex numbers in polar form is similar:
"Divide the r's and subtract the angles":
+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]) )](/cgi-bin/plot-formula.mpl?expression=%28++r%5B1%5D%28+cos%28A%5B1%5D%29%2Bi%2Asin%28A%5B1%5D%29+%29++%29%2F%28++r%5B2%5D%28+cos%28B%5B2%5D%29%2Bi%2Asin%28B%5B2%5D%29+%29++%29+=%0D%0A%28r%5B1%5D%2Fr%5B2%5D%29%28+cos%28A%5B1%5D-B%5B2%5D%29%2Bi%2Asin%28A%5B1%5D-B%5B2%5D%29+%29++&x=0003)
Choice 2.
Edwin
