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