Let Z and W be complex numbers such that ∣ Z ∣ = ∣ W ∣ , and ar g Z denotes the principal argument of Z . Statement 1:If ar g Z + ar g W = π , then Z = − W ˉ . Statement 2: ∣ Z ∣ = ∣ W ∣ , implies arg

Question

Let Z and W be complex numbers such that ∣ Z ∣ = ∣ W ∣ , and ar g Z denotes the principal argument of Z . Statement 1:If ar g Z + ar g W = π , then Z = − W ˉ . Statement 2: ∣ Z ∣ = ∣ W ∣ , implies arg Z − ar g W ˉ = π .

TestHub · Accepted Answer

Let ∣ Z ∣ = ∣ W ∣ = r ⇒ Z = r e i θ , W = r e i ϕ where θ + ϕ = π ∴ W ˉ = r e − i ϕ Now, Z = r e i ( π − ϕ ) = r e iπ × e − i ϕ = − r e − i ϕ = − W ˉ Thus, statement-1 is true but statement- 2 is false.

Mathematics - Complex Number Question with Solution | TestHub

Options:

Doubts & Discussion