Convert into the polar form : 1 - sin alpha + i cos alpha (no any links, I want exact - Maths - Complex Numbers and Quadratic Equations

Question

Convert into the polar form : 1 - sin alpha + i cos alpha (no any
links, I want exact answer) I have already asked the question but
was disappointed to see the answer

Ishwarmani · Accepted Answer

Dear Student,

Please find below the solution to the asked query:

We have,z=1-sinα+icosα=sin2α2+cos2α2-2sinα2cosα2+icos2α2-sin2α2=cosα2-sinα22+icosα2-sinα2cosα2+sinα2=cosα2-sinα2cosα2-sinα2+icosα2+sinα2=2cosα2-sinα212cosα2-12sinα2+i12cosα2+12sinα2=2cosα2-sinα2sinπ4cosα2-cosπ4sinα2+icosπ4cosα2+sinπ4sinα2⇒z=2cosα2-sinα2sinπ4-α2+icosπ4-α2, which is a polar formHere, r=z=2cosα2-sinα2 and argz=π4-α2

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Convert into the polar form : 1 - sin alpha + i cos alpha (no any links, I want exact answer) I have already asked the question but was disappointed to see the answer