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# If u = (1 + i ) and v = (1 − i ), what is uv?

A complex number is the sum of a real number and an imaginary number.

## Answer: If u = (1 + i ) and v = (1 − i ), the value of uv is 2.

Go through the steps to find the exact value.

**Explanation:**

Given two complex numbers:

u = (1 + i), v = (1 - i)

To calculate uv, let's multiply both the complex numbers.

uv = (1 + i)(1 - i)

Using the algebraic identity (a + b)(a - b) = a^{2} - b^{2},

⇒ uv = 1^{2} - i^{2}

⇒ uv = 1 - (-1) [Since, i^{2} = -1]

⇒ uv = 1 + 1

Hence, uv = 2

### Thus, if u = (1 + i ) and v = (1 − i ), the value of uv is 2.

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