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How to I convert -i into polar form? 

 May 11, 2020

Best Answer 

 #3
avatar+20906 
+1

Complex number form:  x + yi.

 

The number i can be written in the complex number form of 0 -1i.

 

To rewrite this number into r·cis( theta ) form, use these two formulas:

  r  =  sqrt( x2 + y2 )     and     theta  =  tan-1( y/x ).

 

For this problem:  x = 0   and  y = -1.

   r  =  sqrt( x2 + y2 )   =  sqrt( (0)2 + (-1)2 )  =  sqrt( 0 + 1 )  =  sqrt( 1 )  =  1

 

  theta  =  tan-1( -1/ 0 )  =  undefined   --->   But, if you were to graph 0 - 1i, the point would be on the negative y-axis,

  therefore,  theta  = 270o  (or, in radian form, 3pi/2).

 

r·cis( theta )  =  1·cis( 270o )

 May 11, 2020
 #3
avatar+20906 
+1
Best Answer

Complex number form:  x + yi.

 

The number i can be written in the complex number form of 0 -1i.

 

To rewrite this number into r·cis( theta ) form, use these two formulas:

  r  =  sqrt( x2 + y2 )     and     theta  =  tan-1( y/x ).

 

For this problem:  x = 0   and  y = -1.

   r  =  sqrt( x2 + y2 )   =  sqrt( (0)2 + (-1)2 )  =  sqrt( 0 + 1 )  =  sqrt( 1 )  =  1

 

  theta  =  tan-1( -1/ 0 )  =  undefined   --->   But, if you were to graph 0 - 1i, the point would be on the negative y-axis,

  therefore,  theta  = 270o  (or, in radian form, 3pi/2).

 

r·cis( theta )  =  1·cis( 270o )

geno3141 May 11, 2020
 #4
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+1

That makes sense! Thank you so much! 

Guest May 11, 2020

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