Question

Reduce 1 - cosx + isinx to the modules amplitude form​

Answer 1

Given :   1 - cosx + isinx  

To Find : Reduce 1 - cosx + isinx to the modulus amplitude form​

Solution:

modulus  amplitude form​

z=∣z∣(cosθ+isinθ)

1 - cosx + isinx  

= 2sin²(x/2)  + i (2sin(x/2)cos(x/2)

= 2sin(x/2) ( sin(x/2)  +  icos(x/2))

=  2sin(x/2) (cos(π/2 - x/2)  +  iSin(π/2 - x/2))

2sin(x/2) (cos(π/2 - x/2)  +  iSin(π/2 - x/2)) is the required form

∣z∣ = 2sin(x/2)

cosθ+isinθ = cos(π/2 - x/2)  +  iSin(π/2 - x/2)

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