Let Z and W be complex numbers such that |Z| = |W|, and arg Z denotes the principal argument of Z. Statement 1:If arg Z + arg W = p, then Z W = - . Statement 2: |Z| = |W|, implies arg Z

Question:
Let $Z$ and $W$ be complex numbers such that $|Z|=|W|$, and arg $Z$ denotes the principal argument of $Z$.
Statement 1:If $\arg Z+\arg W=\pi$, then $Z=-\bar{W}$.
Statement 2: $|Z|=\mid W$, implies $\arg Z-\arg \bar{W}=\pi$.

Statement 1 is true, Statement 2 is false.
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1 .
Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1 .
Statement 1 is false, Statement 2 is true.

Correct Option: 1

JEE Main Previous Year 1 Question of JEE Main from Mathematics Complex Numbers and Quadratic Equations chapter.

JEE Main Previous Year Online May 19, 2012

Solution:

Let Z and W be complex numbers such that |Z| = |W|, and arg Z denotes the principal argument of Z. Statement 1:If arg Z + arg W = p, then Z W = – . Statement 2: |Z| = |W|, implies arg Z – arg W = p.

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