Question

c) Check whether the following pairs of elements are associates:
i) 5+4i and 5-4i.
ii) 5+4i and -4+5i.
iii) 2x2+4x+6 and x2+2x+3.

Answer 1

Answer on Question #44455 – Math - Abstract Algebra

c) Check whether the following pairs of elements are associates:

i) $5 + 4i$ and $5 - 4i$.

ii) $5 + 4i$ and $-4 + 5i$.

iii) $2 \times 2 + 4x + 6$ and $x^2 + 2x + 3$.

Solution

We will use symmetry property for show association:

i. $5 + 4i$ and $5 - 4i$.

This pair of elements is obvious associate, because elements are symmetric for $x$ axis (real axis),

ii. $5 + 4i$ and $-4 + 5i$

There is no symmetry between these elements, so they are not associates.

iii. $2x^{2} + 4x + 6$ and $x^2 + 2x + 3$

We will draw the picture for representation of ours elements:

We can see that the first element is the scaling of second by 2. They are linear dependent, so they can't be associates.

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