find the multiplicative inverse of z=(2+√3i)²​

Question

find the multiplicative inverse of z=(2+√3i)²​

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Emery 1 month 2021-08-12T04:21:12+00:00 1 Answer 0 views 0

Answers ( )

  1. Ava
    0
    2021-08-12T04:22:51+00:00

    Step-by-step explanation:

    Given,

    z =  {(2 +  \sqrt{3}i) }^{2}

     =  > z =  {(2)}^{2}  +  {( \sqrt{3}i) }^{2}  + 2.2. (\sqrt{3}) i

    z = 4 - 3 + (4 \sqrt{3}) i

     =  > z = 1 + (4 \sqrt{3}) i

    So,

     {z}^{ - 1} =   \frac{1}{1 + 4 \sqrt{3} i }

     =  >  {z}^{ - 1}  =  \frac{1 - 4 \sqrt{3}i }{(1 + 4 \sqrt{3}i)(1 - 4 \sqrt{3} i) }

     =  >  {z}^{ - 1}  =  \frac{1 - 4 \sqrt{3} i}{1 + 48}

     =  >  {z}^{ - 1} =  \frac{1}{49} -  \frac{4 \sqrt{3} }{49} i

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