Question

Match each expression to its equivalent standard form.

A. x^2 + x + 2
B. x^2 + 2x + 2
C. x^2 + 4
D. x^2 - 4x + 8
E. x^2 +16
F. x^2 - 4x -4

(x + 2i)(x - 2i)
(x - 2 + 2i)(x - 2 - 2i)
(x + 1 + i)(x + 1 - i)
a) A-3, B-1, C-5, D-2, E-4, F-6
b) A-3, B-1, C-2, D-4, E-5, F-6
c) A-6, B-2, C-5, D-4, E-1, F-3
d) A-1, B-2, C-3, D-4, E-5, F-6

Answer 1

The equivalent standard forms of the given complex number expressions are determined by expanding and simplifying them. Matches are C for (x + 2i)(x - 2i), F for (x - 2 + 2i)(x - 2 - 2i), and B for (x + 1 + i)(x + 1 - i), leading to option b) as the correct answer.

Step-by-step explanation:

The task here is to match each expression with its equivalent in standard form. By expanding and simplifying the given expressions, we can find their standard forms:

1. (x + 2i)(x - 2i) simplifies to x2 - (2i)2 which equals x2 + 4, matching with expression C.
2. (x - 2 + 2i)(x - 2 - 2i) simplifies to x2 - 4x + 4 + (2i)2 which equals x2 - 4x matching with expression F.
3. (x + 1 + i)(x + 1 - i) simplifies to x2 + 2x + 1 + (i)2 which is x2 + 2x + 1 - 1 or x2 + 2x, so it matches with expression B.

By matching these expansions to the expressions given in standard form, we determine that the correct answer is option b) A-3, B-1, C-5, D-4, E-2, F-6.