JEE Advanced Mathematics question
Let , be two unimodular complex numbers such that . If , then
Answer: (D)
Solution
z_1\bar z_2=(a+ib)(p-iq)=(ap+bq)+i(bp-aq), so .
ω_1ω_2=(a+ip)(b-iq)=(ab+pq)+i(bp-aq)⇒Im(ω_1ω_2)=bp-aq=1.
So (d) holds.
Why the others fail: write , (unimodular). Then
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