If = (a + ib), find the values of a and b.

Given:

Consider the given equation,

Now, we rationalize

[Here, we multiply and divide by the conjugate of 1 + i]

Using (a + b)(a – b) = (a² – b²)

[∵ i² = -1]

= (-i)¹⁰⁰

= [(-i)⁴]²⁵

= (i⁴)²⁵

= (1)²⁵

[∵ i⁴ = i² × i² = -1 × -1 = 1]

(a + ib) = 1 + 0i

On comparing both the sides, we get

a = 1 and b = 0

hence, the value of a is 1 and b is 0