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If z = re iΘ , then the value of |e iz | is equal to- e -rcosΘ e rcosΘ e -rsinΘ e rsinΘ Please answer quick....

If z = reiΘ , then the value of |eiz| is equal to-
  1. e-rcosΘ
  2. ercosΘ
  3. e-rsinΘ
  4. ersinΘ
Please answer quick....

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Mohit
 
I have written theta as @ because of simplicity in writing.
 
e^i(re^i@)
= e ^i(r cos@ + i sin@)
= e ^ (i r cos@ - sin@)
= e ^-sin@ *  e^i r cos@
Now |e^iz| = e^-sin@  * |e^i r cos@|
= e-sin @        (because |ei r cos@| = 1)
Hence option C is correct.
 
 
Regards
Arun (askIITians forum expert)

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