Simplify: (1 + i)(1 - i)
Answer
a. -2i
b. 2
c. 2i
d.-2
(1)(1 - i) + (i)(1 - i)
now simplify.
note: i^2=-1
1 - i + i -i^2 = 1 - (-1) = ?
To simplify the expression (1 + i)(1 - i), we can use the distributive property of multiplication, which states that (a + b)(c + d) = ac + ad + bc + bd.
In this case, let's apply the distributive property:
(1 + i)(1 - i) = 1(1) + 1(-i) + i(1) + i(-i)
Now we simplify each term:
1(1) = 1
1(-i) = -i
i(1) = i
i(-i) = -i^2
Remember that i^2 is equal to -1, so we substitute:
-1
Now we sum up all the terms:
1 - i + i - i^2 = 1 - i + i -(-1) = 1 - i + i + 1
Since the i terms cancel each other out, we are left with:
1 + 1 = 2
Therefore, the simplified expression is 2.
The correct answer is b. 2.