Question

Find the multiplicative
invesse
of (2+i√3)^2​

Answer 1

I hope it will help you

Answer 2

Answer:

(1-i 4√3) / 49

Step-by-step explanation:

(2+i√3)²

= 2² + 2. 2. i√3 + (i.√3)²

= 4 + i. 4√3 + (-1) . 3

= 4-3+ i. 4√3

= 1+i 4√3

therefore, multiplicative inverse of 1+i 4√3 is 1 / (1+i 4√3)

1 / (1+i 4√3) = 1 / (1+i 4√3) *  (1-i 4√3) /  (1-i 4√3)

                   =  (1-i 4√3) / (1+i 4√3)(1-i 4√3)

                  =  (1-i 4√3) / 1² - (i4√3)²

                  = (1-i 4√3) / 1 - (-1)(16)(3)

                 = (1-i 4√3) / 1 +48

                 = (1-i 4√3) / 49