Math Is Fun Forum

glenn101

Member

Registered: 2008-04-02

Posts: 108

Complex Numbers

How would I explain ircistheta geometrically?
I don't know where to start.
Any help would be appreciated:)
oh and cis means costheta+isintheta.

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Complex Numbers

do you mean:

in which case, remember that r.cisθ is one way of writing a complex number in polar form, such that it's a point 'r' distance from the origin at an angle θ counterclockwise to the x-axis

multiplying by i is the same as rotating that point a further 90 degrees about the x-axis, in otherwords:
ir.cisθ gives you a point on the argand diagram 'r' units from the origin, at an angle (θ+½π)rad or (θ+90°)degrees counterclockwise from the x-axis.

To see this note that you can see this by remembering that i is at 90 degrees = ½π radians from x-axis counterclockwise, so writing in exponential form you can write the expression as:

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