Question 35491
<pre><font size = 4><b>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( 200, 200, -5, 5, -5, 5, -sqrt(x^2/x)sqrt(x)/5) }}}(5,-1) 

so x=5, y=-1  

<font face = "symbol">q</font> = tan<sup>-1</sup>(y/x) in Q4 = tan-1(-1/5) in Q4. By calculator,

tan<sup>-1</sup>(1/5) = 11.3°, so to get the angle in Q4 we subtract from 360°
and get <font face = "symbol">q</font> = 348.7°
     _____    __________    ____    __
r = <font face = "symbol">Ö</font>x²+y² = <font face = "symbol">Ö</font>(5)²+(-1)² = <font face = "symbol">Ö</font>25+1 = <font face = "symbol">Ö</font>26
                    __
r(cos<font face = "symbol">q</font> + i·sin<font face = "symbol">q</font>) = <font face = "symbol">Ö</font>26(cos348.7° + i·sin348.7°)
 
Edwin McCravy
AnlytcPhil@aol.com</pre>