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2.38. Consider the imaginary number a - ib = sqrt((p - iq)/(r - ls)) what is the value of (x ^ 2 y ^ 2) ^ 2 ? A] p^ 2 -q^ 2 r^ 2 -s^ 2 where i = sqrt(- 1) [B] [C] Information is inadequate to answer this question. (p ^ 2 q ^ 2)/(r ^ 2 s ^ 2) [D] None of the above.?
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2.38. Consider the imaginary number a - ib = sqrt((p - iq)/(r - ls)) w...
Given:
The imaginary number a - ib = sqrt((p - iq)/(r - ls)), where i = sqrt(-1)
To find:
The value of (x^2 + y^2)^2
Solution:
Let's calculate the given imaginary number step by step.
1. Squaring both sides of the equation, we get:
(a - ib)^2 = (p - iq)/(r - ls)
2. Expanding the left side of the equation:
a^2 - 2aib + (ib)^2 = (p - iq)/(r - ls)
3. Simplifying the left side:
a^2 - 2aib - b^2 = (p - iq)/(r - ls)
4. Since i^2 = -1, we can substitute -b^2 with b^2:
a^2 - 2aib + b^2 = (p - iq)/(r - ls)
5. Multiplying both sides of the equation by (r - ls):
(a^2 - 2aib + b^2)(r - ls) = (p - iq)
6. Expanding the left side of the equation:
a^2r - la^2s - 2aibr + 2abis^2 + b^2r - b^2ls = p - iq
7. Grouping real and imaginary terms:
(a^2r - b^2ls) + (-la^2s + 2abis^2) + (-2aibr + b^2r) = p - iq
8. Equating real and imaginary parts on both sides of the equation:
Real part: a^2r - b^2ls - 2aibr + b^2r = p
Imaginary part: -la^2s + 2abis^2 = -q
Now, let's calculate the value of (x^2 + y^2)^2 using the given equation.
9. We know that x = a^2r - b^2ls, y = -2aibr + b^2r, p = a^2r - b^2ls, and q = -la^2s + 2abis^2.
10. Substituting the values of p and q in terms of x and y:
x = p
y = q
11. Taking the square of (x^2 + y^2):
(x^2 + y^2)^2 = (p^2 + q^2)^2
Therefore, the value of (x^2 + y^2)^2 is (p^2 + q^2)^2, which corresponds to option [B].
The imaginary number a - ib = sqrt((p - iq)/(r - ls)), where i = sqrt(-1)
To find:
The value of (x^2 + y^2)^2
Solution:
Let's calculate the given imaginary number step by step.
1. Squaring both sides of the equation, we get:
(a - ib)^2 = (p - iq)/(r - ls)
2. Expanding the left side of the equation:
a^2 - 2aib + (ib)^2 = (p - iq)/(r - ls)
3. Simplifying the left side:
a^2 - 2aib - b^2 = (p - iq)/(r - ls)
4. Since i^2 = -1, we can substitute -b^2 with b^2:
a^2 - 2aib + b^2 = (p - iq)/(r - ls)
5. Multiplying both sides of the equation by (r - ls):
(a^2 - 2aib + b^2)(r - ls) = (p - iq)
6. Expanding the left side of the equation:
a^2r - la^2s - 2aibr + 2abis^2 + b^2r - b^2ls = p - iq
7. Grouping real and imaginary terms:
(a^2r - b^2ls) + (-la^2s + 2abis^2) + (-2aibr + b^2r) = p - iq
8. Equating real and imaginary parts on both sides of the equation:
Real part: a^2r - b^2ls - 2aibr + b^2r = p
Imaginary part: -la^2s + 2abis^2 = -q
Now, let's calculate the value of (x^2 + y^2)^2 using the given equation.
9. We know that x = a^2r - b^2ls, y = -2aibr + b^2r, p = a^2r - b^2ls, and q = -la^2s + 2abis^2.
10. Substituting the values of p and q in terms of x and y:
x = p
y = q
11. Taking the square of (x^2 + y^2):
(x^2 + y^2)^2 = (p^2 + q^2)^2
Therefore, the value of (x^2 + y^2)^2 is (p^2 + q^2)^2, which corresponds to option [B].
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2.38. Consider the imaginary number a - ib = sqrt((p - iq)/(r - ls)) what is the value of (x ^ 2 y ^ 2) ^ 2 ? A] p^ 2 -q^ 2 r^ 2 -s^ 2 where i = sqrt(- 1) [B] [C] Information is inadequate to answer this question. (p ^ 2 q ^ 2)/(r ^ 2 s ^ 2) [D] None of the above.?
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2.38. Consider the imaginary number a - ib = sqrt((p - iq)/(r - ls)) what is the value of (x ^ 2 y ^ 2) ^ 2 ? A] p^ 2 -q^ 2 r^ 2 -s^ 2 where i = sqrt(- 1) [B] [C] Information is inadequate to answer this question. (p ^ 2 q ^ 2)/(r ^ 2 s ^ 2) [D] None of the above.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 2.38. Consider the imaginary number a - ib = sqrt((p - iq)/(r - ls)) what is the value of (x ^ 2 y ^ 2) ^ 2 ? A] p^ 2 -q^ 2 r^ 2 -s^ 2 where i = sqrt(- 1) [B] [C] Information is inadequate to answer this question. (p ^ 2 q ^ 2)/(r ^ 2 s ^ 2) [D] None of the above.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2.38. Consider the imaginary number a - ib = sqrt((p - iq)/(r - ls)) what is the value of (x ^ 2 y ^ 2) ^ 2 ? A] p^ 2 -q^ 2 r^ 2 -s^ 2 where i = sqrt(- 1) [B] [C] Information is inadequate to answer this question. (p ^ 2 q ^ 2)/(r ^ 2 s ^ 2) [D] None of the above.?.
2.38. Consider the imaginary number a - ib = sqrt((p - iq)/(r - ls)) what is the value of (x ^ 2 y ^ 2) ^ 2 ? A] p^ 2 -q^ 2 r^ 2 -s^ 2 where i = sqrt(- 1) [B] [C] Information is inadequate to answer this question. (p ^ 2 q ^ 2)/(r ^ 2 s ^ 2) [D] None of the above.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 2.38. Consider the imaginary number a - ib = sqrt((p - iq)/(r - ls)) what is the value of (x ^ 2 y ^ 2) ^ 2 ? A] p^ 2 -q^ 2 r^ 2 -s^ 2 where i = sqrt(- 1) [B] [C] Information is inadequate to answer this question. (p ^ 2 q ^ 2)/(r ^ 2 s ^ 2) [D] None of the above.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2.38. Consider the imaginary number a - ib = sqrt((p - iq)/(r - ls)) what is the value of (x ^ 2 y ^ 2) ^ 2 ? A] p^ 2 -q^ 2 r^ 2 -s^ 2 where i = sqrt(- 1) [B] [C] Information is inadequate to answer this question. (p ^ 2 q ^ 2)/(r ^ 2 s ^ 2) [D] None of the above.?.
Solutions for 2.38. Consider the imaginary number a - ib = sqrt((p - iq)/(r - ls)) what is the value of (x ^ 2 y ^ 2) ^ 2 ? A] p^ 2 -q^ 2 r^ 2 -s^ 2 where i = sqrt(- 1) [B] [C] Information is inadequate to answer this question. (p ^ 2 q ^ 2)/(r ^ 2 s ^ 2) [D] None of the above.? in English & in Hindi are available as part of our courses for JEE.
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2.38. Consider the imaginary number a - ib = sqrt((p - iq)/(r - ls)) what is the value of (x ^ 2 y ^ 2) ^ 2 ? A] p^ 2 -q^ 2 r^ 2 -s^ 2 where i = sqrt(- 1) [B] [C] Information is inadequate to answer this question. (p ^ 2 q ^ 2)/(r ^ 2 s ^ 2) [D] None of the above.?, a detailed solution for 2.38. Consider the imaginary number a - ib = sqrt((p - iq)/(r - ls)) what is the value of (x ^ 2 y ^ 2) ^ 2 ? A] p^ 2 -q^ 2 r^ 2 -s^ 2 where i = sqrt(- 1) [B] [C] Information is inadequate to answer this question. (p ^ 2 q ^ 2)/(r ^ 2 s ^ 2) [D] None of the above.? has been provided alongside types of 2.38. Consider the imaginary number a - ib = sqrt((p - iq)/(r - ls)) what is the value of (x ^ 2 y ^ 2) ^ 2 ? A] p^ 2 -q^ 2 r^ 2 -s^ 2 where i = sqrt(- 1) [B] [C] Information is inadequate to answer this question. (p ^ 2 q ^ 2)/(r ^ 2 s ^ 2) [D] None of the above.? theory, EduRev gives you an
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