Question

What is the result of multiplication of complex numbers \sqrt(3)+i and (1)/(8)(cos(5\pi )/(3)+isin(5\pi )/(3)) ?

Answer 1

Given :   complex numbers  √3  + i    and   ( 1/8) ( cos ( 5π/3) + i sin(5π/3) )

To Find :  result of multiplication of complex numbers

Solution:

( 1/8) ( cos ( 5π/3) + i sin(5π/3) )

= ( 1/8) (1/2 + i (-√3 / 2)  )

= (1/16) ( 1  - √3 i )

(√3  + i  ) * (1/16) ( 1  - √3 i )

= (1/16)  ( √3   - 3i   + i  - √3 i²)

i² = - 1

=  (1/16)  ( √3   - 2i   + √3  )

=  (1/16)  ( 2(√3   -  i )  )

=  (1/8)    (√3   -  i )  

result of multiplication of given  complex numbers =  (1/8)    (√3   -  i )  

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