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Asked Oct 29, 2019
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[1E q22]

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22. The complex numbers wi and w2 have modulus 1, and arguments ai and a2 respectively,
where 0< a1 < a2 <
Show that Arg (w1 -w2)= (a1+a2-T).
T
2
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22. The complex numbers wi and w2 have modulus 1, and arguments ai and a2 respectively, where 0< a1 < a2 < Show that Arg (w1 -w2)= (a1+a2-T). T 2

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Expert Answer

Step 1

To prove the equality of the two angles , under the given conditions

Step 2

Writing down U, V in the usual form ...

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Let U,V be complex numbers,with UHV1, and arg (U) = u,arg(V) = v. with 0<u<v< 2 Then U U |e" = e" = cosu+isinu similarly,V cos v+ isinv.

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