Relations and Functions

Relations and Functions

Question

Find the multiplicative inverse of each of the complex number.


space space space space space space space space space space space space square root of 5 plus space 3 straight i

Answer

Z  = space space space space space space space space space space square root of 5 plus 3 straight i
Multiplicative inverse of z  = space space space space space space space space space 1 over straight z    = space space space space space space space space space space space space space space space space space space space space space space fraction numerator 1 over denominator square root of 5 plus 3 straight i end fraction equals fraction numerator 1 over denominator square root of 5 plus 3 straight i end fraction straight x fraction numerator square root of 5 minus 3 straight i over denominator square root of 5 minus 3 straight i end fraction

                              space space space space space space space space space space space space space space space space space space space equals space space fraction numerator square root of 5 minus space 3 straight i over denominator left parenthesis square root of 5 right parenthesis squared space minus left parenthesis 3 straight i right parenthesis squared end fraction equals fraction numerator square root of 5 minus 3 straight i over denominator 5 space plus space 9 end fraction space equals space fraction numerator square root of 5 over denominator 14 end fraction minus 3 over 14 straight i

More Chapters from Relations and Functions