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If u =(1 + i√3) and v=(1-i√3) , what is UV?
a.1
b.-4i
c.0
d.4

User Alex Ilyin
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1 Answer

1 vote

Final answer:

The product of u and v is -2.Applying the distributive property, the product of (1 + i√3)(1 - i√3) simplifies to -2. The calculation involves eliminating cross-products and recognizing the square of the imaginary term. Option B is the correct answer.

Step-by-step explanation:

To find the product of u and v, we can use the distributive property of multiplication over addition. This means we multiply each term of u by each term of v and combine like terms. Let's perform the calculation:

(1 + i√3)(1 - i√3) = 1 - i√3 + i√3 - (i√3)(i√3)

Using the fact that (i√3)(i√3) = -3, we simplify further:

= 1 - 3 = -2

Therefore, the product of u and v is -2.

To determine the product of u and v, apply the distributive property. Multiply each term of u by each term of v and simplify. The calculation results in (1 + i√3)(1 - i√3) = 1 - i√3 + i√3 - (i√3)(i√3). Recognizing that (i√3)(i√3) = -3, the expression further simplifies to 1 - 3 = -2. Thus, the product of u and v is -2.

User YourMJK
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