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Let z be any non - zero complex number. Then arg(z) + arg(z¯) is equal to
- a)-π
- b)π
- c)0
- d)π/2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let z be any non - zero complex number. Then arg(z) +arg(z¯)is eq...
Let z = x+iy
zˉ = x−iy
arg(z) = xy,arg(zˉ) = −xy
arg(z) + arg(zˉ) = 0
Most Upvoted Answer
Let z be any non - zero complex number. Then arg(z) +arg(z¯)is eq...
arg(x) + 
= 0
= 0Free Test
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Community Answer
Let z be any non - zero complex number. Then arg(z) +arg(z¯)is eq...
Explanation:
- Argument of a complex number:
- The argument of a complex number is the angle that the complex number makes with the positive real axis in the complex plane.
- It is denoted by arg(z) for a complex number z.
- Addition of arguments:
- When we add the arguments of two complex numbers z and z̅, the angle they make with the positive real axis will be the same.
- So, arg(z) + arg(z̅) will be equal to the angle that z makes with the positive real axis.
- Complex conjugate:
- The complex conjugate of a complex number z = a + bi is z̅ = a - bi, where a and b are real numbers.
- The complex conjugate is obtained by changing the sign of the imaginary part.
- Sum of arguments for z and z̅:
- Since z and z̅ lie on the opposite sides of the real axis, their arguments are negatives of each other.
- Therefore, arg(z) + arg(z̅) = arg(z) - arg(z) = 0.
Therefore, the sum of the arguments of a non-zero complex number z and its complex conjugate z̅ is equal to 0.
- Argument of a complex number:
- The argument of a complex number is the angle that the complex number makes with the positive real axis in the complex plane.
- It is denoted by arg(z) for a complex number z.
- Addition of arguments:
- When we add the arguments of two complex numbers z and z̅, the angle they make with the positive real axis will be the same.
- So, arg(z) + arg(z̅) will be equal to the angle that z makes with the positive real axis.
- Complex conjugate:
- The complex conjugate of a complex number z = a + bi is z̅ = a - bi, where a and b are real numbers.
- The complex conjugate is obtained by changing the sign of the imaginary part.
- Sum of arguments for z and z̅:
- Since z and z̅ lie on the opposite sides of the real axis, their arguments are negatives of each other.
- Therefore, arg(z) + arg(z̅) = arg(z) - arg(z) = 0.
Therefore, the sum of the arguments of a non-zero complex number z and its complex conjugate z̅ is equal to 0.
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