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The square root of the number 5 + 12i is
- a)(3 + 2i)
- b)(3 - 2i)
- c)
(3 + 2i) - d)none
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The square root of the number 5 + 12i isa)(3 + 2i)b)(3 - 2i)c) (3 + 2i...
Ans.
Option (c)
Suppose that a+bi is a square root of 5 + 12i.
Then, (a+bi)^2 = (a^2 - b^2) + (2ab)i = 5 + 12i.
Equate real and imaginary parts:
a^2 - b^2 = 5
2ab = 12 ==> b = 6/a.
So, a^2 - (6/a)^2 = 5
==> a^2 - 36/a^2 = 5
==> a^4 -5a^2 - 36 = 0.
==> (a^2 -9)(a^2 + 4) = 0.
Since a must be real, a = 3 or -3.
This gives b = 2 or -2, respectively.
Thus, we have two square roots: 3+2i or -3-2i.
Then, (a+bi)^2 = (a^2 - b^2) + (2ab)i = 5 + 12i.
Equate real and imaginary parts:
a^2 - b^2 = 5
2ab = 12 ==> b = 6/a.
So, a^2 - (6/a)^2 = 5
==> a^2 - 36/a^2 = 5
==> a^4 -5a^2 - 36 = 0.
==> (a^2 -9)(a^2 + 4) = 0.
Since a must be real, a = 3 or -3.
This gives b = 2 or -2, respectively.
Thus, we have two square roots: 3+2i or -3-2i.
Most Upvoted Answer
The square root of the number 5 + 12i isa)(3 + 2i)b)(3 - 2i)c) (3 + 2i...
Ans.
Option (c)
Suppose that a+bi is a square root of 5 + 12i.
Then, (a+bi)^2 = (a^2 - b^2) + (2ab)i = 5 + 12i.
Equate real and imaginary parts:
a^2 - b^2 = 5
2ab = 12 ==> b = 6/a.
So, a^2 - (6/a)^2 = 5
==> a^2 - 36/a^2 = 5
==> a^4 -5a^2 - 36 = 0.
==> (a^2 -9)(a^2 + 4) = 0.
Since a must be real, a = 3 or -3.
This gives b = 2 or -2, respectively.
Thus, we have two square roots: 3+2i or -3-2i.
Read more on Brainly.in - https://brainly.in/question/240129#readmore
Then, (a+bi)^2 = (a^2 - b^2) + (2ab)i = 5 + 12i.
Equate real and imaginary parts:
a^2 - b^2 = 5
2ab = 12 ==> b = 6/a.
So, a^2 - (6/a)^2 = 5
==> a^2 - 36/a^2 = 5
==> a^4 -5a^2 - 36 = 0.
==> (a^2 -9)(a^2 + 4) = 0.
Since a must be real, a = 3 or -3.
This gives b = 2 or -2, respectively.
Thus, we have two square roots: 3+2i or -3-2i.
Read more on Brainly.in - https://brainly.in/question/240129#readmore
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The square root of the number 5 + 12i isa)(3 + 2i)b)(3 - 2i)c) (3 + 2i)d)noneCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The square root of the number 5 + 12i isa)(3 + 2i)b)(3 - 2i)c) (3 + 2i)d)noneCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The square root of the number 5 + 12i isa)(3 + 2i)b)(3 - 2i)c) (3 + 2i)d)noneCorrect answer is option 'C'. Can you explain this answer?.
The square root of the number 5 + 12i isa)(3 + 2i)b)(3 - 2i)c) (3 + 2i)d)noneCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The square root of the number 5 + 12i isa)(3 + 2i)b)(3 - 2i)c) (3 + 2i)d)noneCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The square root of the number 5 + 12i isa)(3 + 2i)b)(3 - 2i)c) (3 + 2i)d)noneCorrect answer is option 'C'. Can you explain this answer?.
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