find multiplicative inverse of i(2+3i)(3+2i)/5+i
Answers

Answer:
or
Step-by-step explanation:
Given:- The given expression is ( i (2 + 3i) (3 + 2i) )/(5 + i).
To Find:- Multiplicative Inverse of the above expression.
Solution:-
Multiplicative inverse of a number is a number which when multiplied by the original number yields the result 1 i.e. multiplicative identity. It is also called Reciprocal of a number. It is denoted by or
.
The expression is ( i (2 + 3i) (3 + 2i) )/ (5 + i)
= ( (2i + 3i²)(3 + 2i) ) ÷ (5 + i)
= (6i + 9i³ + 4i² + 6i³) ÷ (5 + i)
= (15i³ + 4i² + 6i) ÷ (5 + i)
Simplified form of the given expression is .
Now, the multiplicative of the fraction will be
=
Therefore, multiplicative inverse of ( i (2 + 3i) (3 + 2i) )/ (5 + i) is or
.
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