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) = a² - b²,

⇒ uv = 1² - i²

⇒ uv = 1 - (-1) [Since, i² = -1]

⇒ uv = 1 + 1

Hence, uv = 2

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