Question

In the complex plane, if the points A and B represent $(1 + i)$ and $(-1 + i)$ then the angle between OA and OB is

• A. $3\pi/4$
• B. $\pi$
• C. $\pi/4$
• D. $\pi/2$

Hint:

Plotting points on an Argand diagram often makes the angle between them visually obvious.

Answer 1

The Correct Option is D

Step 1: Concept
The angle between two points $z_{1}$ and $z_{2}$ from the origin is given by $\text{arg}(z_{2}) - \text{arg}(z_{1})$.

Step 2: Meaning
$z_{A} = 1 + i$ lies in the first quadrant with $\text{arg}(z_{A}) = \tan^{-1}(1/1) = \pi/4$.

Step 3: Analysis
$z_{B} = -1 + i$ lies in the second quadrant with $\text{arg}(z_{B}) = \pi - \tan^{-1}(1/1) = 3\pi/4$.

Step 4: Conclusion
The angle between them is $3\pi/4 - \pi/4 = 2\pi/4 = \pi/2$. Final Answer: (D)