SOLUTION: given x + iy form, write in polar form: 5-i

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Question 35491: given x + iy form, write in polar form: 5-i
Answer by AnlytcPhil(1808) About Me  (Show Source):
You can put this solution on YOUR website!
given x + iy form, write in polar form: 5-i

5 - i

A + Bi is represented by the vector whose tail is at (0,0)
and whose head is at (A,B)

5 - i, then, is represented by the vector whose tail is at (0,0)
and whose head is at (5,-1)
+graph%28+200%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+-sqrt%28x%5E2%2Fx%29sqrt%28x%29%2F5%29+(5,-1) 

so x=5, y=-1  

q = tan-1(y/x) in Q4 = tan-1(-1/5) in Q4. By calculator,

tan-1(1/5) = 11.3°, so to get the angle in Q4 we subtract from 360°
and get q = 348.7°
     _____    __________    ____    __
r = Öx²+y² = Ö(5)²+(-1)² = Ö25+1 = Ö26
                    __
r(cosq + i·sinq) = Ö26(cos348.7° + i·sin348.7°)
 
Edwin McCravy
AnlytcPhil@aol.com