Question

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

Answer 1

I hope it will help you.

Answer 2

Answer:

$\frac{5 + i}{15i^{3} + 4i^{2}+6i }$ or $\frac{5 + i}{ ( i (2 + 3i) (3 + 2i) ) }$

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 $\frac{1}{x}$ or $x^{-1}$.

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 $\frac{15i^{3} + 4i^{2}+6i }{5 + i}$.

Now, the multiplicative of the fraction $\frac{15i^{3} + 4i^{2}+6i }{5 + i}$ will be

$\frac{1}{\frac{15i^{3} + 4i^{2}+6i }{5 + i}}$ = $\frac{5 + i}{15i^{3} + 4i^{2}+6i }$

Therefore, multiplicative inverse of ( i (2 + 3i) (3 + 2i) )/ (5 + i) is $\frac{5 + i}{15i^{3} + 4i^{2}+6i }$ or $\frac{5 + i}{ ( i (2 + 3i) (3 + 2i) ) }$.

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