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In the Argand plane if O, P, Q represent respectively the origin, the complex number z and z + iz, then angle OPQ is
- a)π/4
- b)π/3
- c)π/2
- d)2π/3
Correct answer is option 'C'. Can you explain this answer?
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In the Argand plane if O, P, Q represent respectively the origin, the ...
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In the Argand plane if O, P, Q represent respectively the origin, the ...
To find the angle OPQ, we need to find the argument (or angle) of the complex number z and z * iz.
Let's say z = a + bi, where a and b are real numbers.
The complex number z * iz can be written as (a + bi)(-b + ai) = -ab + a^2i - b^2i - abi = (-ab - b^2) + (a^2 - ab)i.
The argument (or angle) of a complex number can be found by taking the arctan of the imaginary part divided by the real part. In this case, the argument of z is arctan(b/a) and the argument of z * iz is arctan((a^2 - ab)/(-ab - b^2)).
Therefore, the angle OPQ is arctan((a^2 - ab)/(-ab - b^2)) - arctan(b/a).
Let's say z = a + bi, where a and b are real numbers.
The complex number z * iz can be written as (a + bi)(-b + ai) = -ab + a^2i - b^2i - abi = (-ab - b^2) + (a^2 - ab)i.
The argument (or angle) of a complex number can be found by taking the arctan of the imaginary part divided by the real part. In this case, the argument of z is arctan(b/a) and the argument of z * iz is arctan((a^2 - ab)/(-ab - b^2)).
Therefore, the angle OPQ is arctan((a^2 - ab)/(-ab - b^2)) - arctan(b/a).
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In the Argand plane if O, P, Q represent respectively the origin, the complex number z and z + iz, then angle OPQ isa)π/4b)π/3c)π/2d)2π/3Correct 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 In the Argand plane if O, P, Q represent respectively the origin, the complex number z and z + iz, then angle OPQ isa)π/4b)π/3c)π/2d)2π/3Correct 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 In the Argand plane if O, P, Q represent respectively the origin, the complex number z and z + iz, then angle OPQ isa)π/4b)π/3c)π/2d)2π/3Correct answer is option 'C'. Can you explain this answer?.
In the Argand plane if O, P, Q represent respectively the origin, the complex number z and z + iz, then angle OPQ isa)π/4b)π/3c)π/2d)2π/3Correct 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 In the Argand plane if O, P, Q represent respectively the origin, the complex number z and z + iz, then angle OPQ isa)π/4b)π/3c)π/2d)2π/3Correct 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 In the Argand plane if O, P, Q represent respectively the origin, the complex number z and z + iz, then angle OPQ isa)π/4b)π/3c)π/2d)2π/3Correct answer is option 'C'. Can you explain this answer?.
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