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# Complex Numbers

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100
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How to I convert -i into polar form?

May 11, 2020

#3
+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
+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 )

geno3141 May 11, 2020
#4
+1

That makes sense! Thank you so much!

Guest May 11, 2020