Question

write the multiplicative inverse of root 3 by 2 minus 1 by 2i

Answer 1

i= √(-1)


√3/2 -1/2i

√3/2 - i/2

(√3-i)/2

multiplicative inverse of this

1/(√3-i) /2

= 2/(√3-i)

Answer 2

√3/2  - i/2  is multiplicative inverse of √3 / 2 -  1/2i  

Step-by-step explanation:

a multiplicative inverse  is basically a reciprocal

Multiplicative inverse of number  is the number which if multiplied by number result in 1

multiplicative inverse of  √3 / 2 -  1/2i         = 1/ (√3 / 2 -  1/2i  )

1/ (√3 / 2 -  1/2i  )

multiplying numerator & denominator by 2i

= 2i/(i√3  - 1)

multiplying & diving by  i√3  + 1

= 2i( i√3  + 1) / (( i√3)² - 1²)

now i² = - 1

=2(-√3 + i)/( -3 - 1)

= 2(-√3 + i)/( -4)

=  (-√3 + i)/( -2)

= √3/2  - i/2

√3/2  - i/2  is multiplicative inverse of √3 / 2 -  1/2i  

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