Question

If u=(1+i√3) and v=(1-i√3), what is uv?

Answer 1

Answer: 4

Explanation:

u=(1+i√3) =2 v=(1-i√3)=2 Uv = (2)(2)=4

Answer 2

4

Explanation:

You may recognize these as factors of the difference of two squares:

... a² -b² = (a+b)(a-b)

where a=1 and b=i√3.

Then the product is ...

... 1² -(i√3)² = 1 - 3i² = 1 +3 = 4

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Of course, i = √-1, so i² = -1.