+23246 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 )
+23246 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 )
