what is the meaning of multiplicative inverse and additive inverse?
find the multiplicative and additive inverse of z=4-56i.

Asked by scorpiokarthik99 | 14th Aug, 2015, 11:33: AM

Expert Answer:

A d d i t i v e space i n v e r s e space i s space t h e space e l e m e n t space w h i c h space w h e n space a d d e d space r e s u l t s space i n space a d d i t i v e space i d e n t i t y. F o r space t h e space s e t space o f space i n t e g e r s comma space a d d i t i v e space i d e n t i t y space i s space 0 space a n d space t h e space a d d i t i v e space i n v e r s e space o f space apostrophe a apostrophe space i s space apostrophe minus a apostrophe. C o n s i d e r space t h e space n u m b e r space 5. A d d i t i v e space i n v e r s e space o f space 5 space i s space minus 5 B e c a u s e comma space 5 plus open parentheses negative 5 close parentheses equals 0  S i m i l a r l y comma space M u l t i p l i c a t i v e space i n v e r s e space i s space t h e space e l e m e n t space w h i c h space w h e n space m u l t i p l i e d space r e s u l t s space i n space m u l t i p l i c a t i v e space i d e n t i t y. F o r space t h e space s e t space o f space i n t e g e r s comma space m u l t i p l i c a t i v e space i d e n t i t y space i s space 1 space a n d space t h e space m u l t i p l i c a t i v e space i n v e r s e space o f space apostrophe a apostrophe space i s space apostrophe 1 over a apostrophe. C o n s i d e r space t h e space n u m b e r space a. M u l t i p l i c a t i v e space i n v e r s e space o f space 5 space i s space 1 fifth B e c a u s e comma space 5 cross times open parentheses 1 fifth close parentheses equals 1  W e space k n o w space t h a t space 4 minus 56 i minus 4 plus 456 i equals 0 T h e r e f o r e comma space A d d i t i v e space i n v e r s e space o f space 4 minus 56 i equals negative 4 plus 56 i  M u l t i p l i c a t i v e space i n v e r s e space o f space 4 minus 56 i equals fraction numerator 1 over denominator 4 minus 56 i end fraction cross times fraction numerator 4 plus 56 i over denominator 4 plus 56 i end fraction equals fraction numerator 4 plus 56 i over denominator 4 squared minus open parentheses 56 i close parentheses squared end fraction equals fraction numerator 4 plus 56 i over denominator 4 squared plus 56 squared end fraction equals fraction numerator 4 plus 56 i over denominator 16 plus 3136 end fraction equals fraction numerator 4 plus 56 i over denominator 3152 end fraction equals 4 over 3152 plus fraction numerator 56 i over denominator 3152 end fraction equals 1 over 788 plus fraction numerator 14 i over denominator 788 end fraction

Answered by Vimala Ramamurthy | 15th Aug, 2015, 08:46: AM