MCQ
Let $z$ be a complex number. Then the angle between vectors $z$ and $ - iz$ is
  • A
    $\pi $
  • B
    $0$
  • $ - \frac{\pi }{2}$
  • D
    None of these

Answer

Correct option: C.
$ - \frac{\pi }{2}$
c
(c) Since the multiplication of a complex number by $ - i$ rotates through it by a right angle in negative (clockwise) direction.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

Let $A$ be the point $(1,2)$ and $B$ be any point on the curve $x^2+y^2=16$. If the centre of the locus of the point $P$, which divides the line segment $A B$ in the ratio $3: 2$ is the point $C(\alpha, \beta)$, then the length of the line segment $AC$ is
If $\text{P}\text{(A}\cup\text{B)} = \text{P}\text{(A}\cap\text{B)}$ for any two events A and B, the
If $|{a_k}| < 1,{\lambda _k} \ge 0$ for $k = 1,\,2,....n$ and ${\lambda _1} + {\lambda _2} + ... + {\lambda _n} = 1,$ then the value of $|{\lambda _1}{a_1} + {\lambda _2}{a_2} + ....{\lambda _n}{a_n}|$ is
If $a = \cos (2\pi /7) + i\,\sin (2\pi /7),$ then the quadratic equation whose roots are $\alpha = a + {a^2} + {a^4}$ and $\beta = {a^3} + {a^5} + {a^6}$ is
The sum of the solutions in $x \in (0,4\pi )$ of the equation $4\sin \frac{x}{3}\left( {\sin \left( {\frac{{\pi  + x}}{3}} \right)} \right)\sin \left( {\frac{{2\pi  + x}}{3}} \right) = 1$ is
If $\text{A+B+C}=\pi,$ then $\frac{\tan\text{A}+\tan\text{B}+\tan\text{C}}{\tan\text{A}\tan\text{B}\tan\text{C}}$ is equal to:
The multiplication inverse of a number is the number itself, then its initial value is
Let $A B C$ be an equilateral triangle with side length $a$. Let $R$ and $r$ denote the radii of the circumcircle and the incircle of triangle $A B C$ respectively. Then, as a function of $a$, the ratio $\frac{R}{r}$
A straight line through origin $O$ meets the lines $3y= 10 - 4x$ and $8x + 6y+ 5 = 0$ at points$ A$ and $B$ respectively. Then $O$ divides the segment $AB$ in the ratio
If a line passing through origin touches the circle ${(x - 4)^2} + {(y + 5)^2} = 25$, then its slope should be