Question

Question 12 Find the multiplicative inverse of the complex number 5^(1/2) + 3i

Class X1 - Maths -Complex Numbers and Quadratic Equations Page 104

Answer 1

Here you go!! I have used the formula:
z^-1= conjugate of z/ square of the modulus of z

Answer 2

Let z = √5 + 3i
Then it's multiplicative inverse is 1/z = 1/(√5 + 3i)
Now, rationalize
1/z = (√5 - 3i)/(√5 +3i)(√5-3i)
[Use, a²-b² = (a-b)(a+b)]

= (√5-3i)/{√5²-(3i)²}
=(√5-3i)/(5+9)
=(√5/14)-(3/14)i