Find the modulus of exp ⁡ { i R 2 cos ⁡ ( 2 t ) − R 2 sin ⁡ ( 2 t ) }

Question

Find the modulus of   exp  ⁡  {  i      R    2    cos  ⁡  (  2  t  )  −      R    2    sin  ⁡  (  2  t  )  }

charringpq49u · Accepted Answer

Hint -Write it as                     exp        ⁡        {        i                  R          2                cos        ⁡        (        2        t        )        }                    exp        ⁡        {                  R          2                sin        ⁡        (        2        t        )        }             and recall that       |                            z          1                          z          2                      |    =                              |                          z          1                          |                                      |                          z          2                          |                     and       |    exp  ⁡  {  i  t  }      |    =  1

bedblogi38am · Accepted Answer

HINT:Assuming t is real,      e          −              R        2            sin      ⁡      2      t        ⋅      e          i      (              R        2            cos      ⁡      2      t      )      Now use       |    x  y      |    =      |    x      |        |    y      |   and Euler&#039;s identity to find       |        e          i      (              R        2            cos      ⁡      2      t      )            |    =  1

Find the modulus of exp ⁡ <mo fence="false" stretchy="false">{ i

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