Find the multiplicative inverse of the complex number 4 - 2i.

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We have to find the multiplicative inverse of 4 - 2i.

Now the multiplicative inverse of any number X is defined as X^-1, so that X*X^-1 = 1.

For 4 - 2i, let the multiplicative inverse be M.

Now M* (4 - 2i) = 1

=> M = 1/ (4...

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We have to find the multiplicative inverse of 4 - 2i.

Now the multiplicative inverse of any number X is defined as X^-1, so that X*X^-1 = 1.

For 4 - 2i, let the multiplicative inverse be M.

Now M* (4 - 2i) = 1

=> M = 1/ (4 -2i)

=> M = (4 +2i)/ ( 4- 2i)( 4 +2i)

=> M = (4 + 2i) / [4^2 - (2i)^2]

=> M = ( 4 + 2i) / [ 16 + 4]

=> M = (4 + 2i) / 20

=> M = 4/20 + 2i /20

=> M = 1/5 + i/10

Therefore the multiplicative inverse of 4 - 2i is 1/5 + i/10.

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