Question

Find the angle between the vectors 1 + i and -1 + i

• A. 45
• B. 90
• C. 180
• D. 60

Answer 1

The correct option is B

90

When we say vectors (1+i) and (-1+i), they have the tail at the origin. We will assume we get the vector

(-1+i) by rotating (1+i) through an angle of $\theta$ anticlockwise. So we have the following relation.

$\frac{B}{A}$ = $\left|\frac{B}{A}\right|$ $e^{i\theta }$

|B| = |A| = $\sqrt{2}$

⇒ $e^{i\theta }$ = $\frac{B}{A}$

$\theta$ = Arg $\left(\frac{B}{A}\right)$

= Arg $\left(\frac{-1+i}{1+i}\right)$

= Arg $\left[\frac{i(1+i)}{(1+i)}\right]$

Arg(i)

= $\frac{\pi }{2}$

= ${90}^{\circ }$