How to put 1 cos ⁡ θ − j sin ⁡ θ in the form a+jb? ( j 2 = − 1)

Question

How to put       1          cos      ⁡      θ      −      j      sin      ⁡      θ       in the form a+jb? (      j    2    =  −  1)

extractumzz · Accepted Answer

Hint. One may write, with       j    2    =  −  1,      1          cos      ⁡      θ      −      j      sin      ⁡      θ        =            1      ⋅      (      cos      ⁡      θ      +      j      sin      ⁡      θ      )              (      cos      ⁡      θ      −      j      sin      ⁡      θ      )      (      cos      ⁡      θ      +      j      sin      ⁡      θ      )        .

Jerry Villegas · Accepted Answer

1          cos      ⁡      θ      −      j      sin      ⁡      θ        =            cos      ⁡      θ      +      j      sin      ⁡      θ              (      cos      ⁡      θ      −      j      sin      ⁡      θ      )      (      cos      ⁡      θ      +      j      sin      ⁡      θ      )        =            cos      ⁡      θ      +      j      sin      ⁡      θ                      cos                  2                    ⁡      θ      −              j        2                    sin        2            ⁡      θ        =            cos      ⁡      θ      +      j      sin      ⁡      θ                      cos        2            ⁡      θ      −      (      −      1      )              sin        2            ⁡      θ        =            cos      ⁡      θ      +      j      sin      ⁡      θ                      cos        2            ⁡      θ      +              sin        2            ⁡      θ        =            cos      ⁡      θ      +      j      sin      ⁡      θ        1    =  cos  ⁡  θ  +  j  sin  ⁡  θ

How to put 1 cos ⁡ θ &

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