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

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Correct answer: A. Statement 1 is true, Statement 2 is false.

Let |Z|=| W |=r Z=r e^ i , W =r e^ i where + = W =r e^ -i Now, Z=r e^ i( - ) =r e^ i e^ -i =-r e^ -i =- W Thus, statement-1 is true but statement- 2 is false.

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

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