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If z and ω are two non-zero complex numbers such that |z ω | = 1, and arg(z) - arg(ω)= π/2,then z̅ω is equal to
  • a)
    1
  • b)
    -1
  • c)
    i
  • d)
    -i
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If z and ω are two non-zero complex numbers such that |z ω...
Given Information:
- |zω| = 1
- arg(z) - arg(ω) = π/2

Solution:

Using Polar Form:
- Let z = r1(cosθ1 + isinθ1) and ω = r2(cosθ2 + isinθ2)
- |zω| = |z| |ω| = r1r2 = 1
- arg(zω) = arg(z) + arg(ω) = θ1 + θ2

Given Condition:
- θ1 - θ2 = π/2

Substitute in Polar Form:
- z = r1e^(iθ1) and ω = r2e^(iθ2)
- zω = r1r2e^(i(θ1+θ2))
- θ1 + θ2 = π/2
- zω = r1r2e^(i(π/2)) = r1r2i = i

Conclusion:
Therefore, zω = i, which corresponds to option 'd'.
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If z and ω are two non-zero complex numbers such that |z ω | = 1, and arg(z) - arg(ω)= π/2,then zω is equal toa)1b)-1c)id)-iCorrect answer is option 'D'. Can you explain this answer?
Question Description
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