Solution:

Finding the multiplicative inverse of complex numbers:
• The multiplicative inverse of a complex number is a number that, when multiplied with the given number, gives the result as 1.
• To find the multiplicative inverse of a complex number, we need to divide 1 by the given complex number.

(i) Multiplicative inverse of √5 + 3i:
• Let the given complex number be z = √5 + 3i.
• To find the multiplicative inverse, let w = a + bi be the inverse of z such that zw = 1.
• Multiply z and w: (a + bi)(√5 + 3i) = 1.
• Equating real and imaginary parts, we get two equations: a√5 - 3b = 1 and 3a + b√5 = 0.
• Solve these equations to find the values of a and b, which will give the multiplicative inverse of z.

(ii) Multiplicative inverse of -i:
• Let the given complex number be z = -i.
• To find the multiplicative inverse, let w = a + bi be the inverse of z such that zw = 1.
• Multiply z and w: (a + bi)(-i) = 1.
• Equating real and imaginary parts, we get two equations: -ai - b = 1 and a = 0.
• Solve these equations to find the values of a and b, which will give the multiplicative inverse of z.
By following these steps and solving the equations, you can find the multiplicative inverse of the given complex numbers.