Question

find the multiplicative inverse of 3-4i /5+4i​

Answer 1

Answer:

multiplicative inverse of 3 -4/ 5+4 is 5+4 / 3-4

Answer 2

Given,

The main term is = (3-4i)/(5+4i)

To find,

The multiplicative inverse of the given main term.

Solution,

According to the mathematical properties, the result of the multiplication of a number and it's multiplicative inverse is always 1.

Let, the multiplicative inverse of the main term = x

(Assume x as a variable to do the further mathematical calculations.)

So,as mentioned above,we get that,

(3-4i)/(5+4i) × x = 1

x = 1 × (5+4i)/(3-4i)

x = (5+4i)/(3-4i)

x = (5+4i)/(3-4i) × (3+4i)/(3+4i)

x = (15+12i+20i+16i²)/(9-16i²)

x = (15+32i-16)/(9+16)

x = (-1+32i)/25

x = -1/25 + 32i/25

Hence, the multiplicative inverse of the given main term is (-1/25 + 32i/25)