Question

Write multiplicative inverse of following questions
5+6i/6+5i

Answer 1

((5 + 6i)(6 - 5i))/((6 + 5i)(6 - 5i))

= (60 + 11i)/61

= (60/61) + (11/61)i

1/((60 + 11i)/61)

= 61/(60 + 11i)

= 61(60 - 11i)/((60 + 11i)(60 - 11i))

= (3,660 - 671i)/3,721

= (60/61) - (11/61)i