Question:
Arg z + Arg $ \bar z. ( z \neq 0)$ is
Arg z + Arg $ \bar z. ( z \neq 0)$ is
Updated On: Jun 18, 2024
- 0
- $\pi$
- $\frac {\pi} {2}$
- none of these
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The Correct Option is C
Solution and Explanation
Let $z=re^{i\theta} \therefore \bar{z}=re^{-i\theta}\bigg]$
$\Rightarrow Arg, z+Arg. \bar{z}=\theta-\theta=0$.
$[\because -\pi < \theta \le \pi$ for $Arg \,2]$
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Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
