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a2 + b2
- a)(a + b )(a-b)
- b)(a + ib)(a -ib)
- c)(a + b )(a- ib)
- d)(a + ib )(a - b)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
a2+ b2a)(a + b )(a-b)b)(a + ib)(a -ib)c)(a + b )(a- ib)d)(a + ib )(a -...
(a + ib) x (a - ib)
= a2 - i2b2
we know i2=-1
so, equation becomes a2 -(-1)b2 =
a2 + b2
Most Upvoted Answer
a2+ b2a)(a + b )(a-b)b)(a + ib)(a -ib)c)(a + b )(a- ib)d)(a + ib )(a -...
Explanation:
To understand why the correct answer is option 'B', let's break down the given expression:
(a + ib)(a - ib)
This expression represents the product of a complex number with its conjugate.
Using the FOIL method, we can expand the expression as follows:
(a + ib)(a - ib) = a^2 - iab + iab - i^2b^2
Since i^2 is equal to -1, the expression simplifies to:
a^2 - i^2b^2
Now, we know that i^2 is equal to -1, so:
a^2 - i^2b^2 = a^2 - (-1)b^2
Simplifying further:
a^2 - (-1)b^2 = a^2 + b^2
Therefore, the expression (a + ib)(a - ib) simplifies to a^2 + b^2.
Now, let's look at the given options:
a) (a + b)(a - b)
This option does not match the simplified expression a^2 + b^2, so it is incorrect.
b) (a + ib)(a - ib)
This option matches the simplified expression a^2 + b^2, so it is the correct answer.
c) (a + b)(a - ib)
This option does not match the simplified expression a^2 + b^2, so it is incorrect.
d) (a + ib)(a - b)
This option does not match the simplified expression a^2 + b^2, so it is incorrect.
Conclusion:
The correct answer is option 'B' because it matches the simplified expression a^2 + b^2, which is the result of multiplying a complex number with its conjugate.
To understand why the correct answer is option 'B', let's break down the given expression:
(a + ib)(a - ib)
This expression represents the product of a complex number with its conjugate.
Using the FOIL method, we can expand the expression as follows:
(a + ib)(a - ib) = a^2 - iab + iab - i^2b^2
Since i^2 is equal to -1, the expression simplifies to:
a^2 - i^2b^2
Now, we know that i^2 is equal to -1, so:
a^2 - i^2b^2 = a^2 - (-1)b^2
Simplifying further:
a^2 - (-1)b^2 = a^2 + b^2
Therefore, the expression (a + ib)(a - ib) simplifies to a^2 + b^2.
Now, let's look at the given options:
a) (a + b)(a - b)
This option does not match the simplified expression a^2 + b^2, so it is incorrect.
b) (a + ib)(a - ib)
This option matches the simplified expression a^2 + b^2, so it is the correct answer.
c) (a + b)(a - ib)
This option does not match the simplified expression a^2 + b^2, so it is incorrect.
d) (a + ib)(a - b)
This option does not match the simplified expression a^2 + b^2, so it is incorrect.
Conclusion:
The correct answer is option 'B' because it matches the simplified expression a^2 + b^2, which is the result of multiplying a complex number with its conjugate.
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Community Answer
a2+ b2a)(a + b )(a-b)b)(a + ib)(a -ib)c)(a + b )(a- ib)d)(a + ib )(a -...
B) (a+in) (a-ib)
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a2+ b2a)(a + b )(a-b)b)(a + ib)(a -ib)c)(a + b )(a- ib)d)(a + ib )(a - b)Correct answer is option 'B'. Can you explain this answer?
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