Question
Multiplication of a non zero complex number by $-i$ rotates the point about origin through a right angle in the anti$-$clockwise direction.
✓
Answer
False.
Let $ z = x + iy,$ where $x, y > 0$
$i.e., z$ or point $A(x, y)$ lies in first quadrant. Now$, -iz = -i(x + iy)$
$= -ix - i^2y = y - ix$
Now$,$ point $B(y, -x)$ lies in fourth quadrant. Also$, \angle AOB = 90^\circ$
Thus$, B$ is obtained by rotating $A$ in clockwise direction about origin.
Let $ z = x + iy,$ where $x, y > 0$
$i.e., z$ or point $A(x, y)$ lies in first quadrant. Now$, -iz = -i(x + iy)$
$= -ix - i^2y = y - ix$
Now$,$ point $B(y, -x)$ lies in fourth quadrant. Also$, \angle AOB = 90^\circ$
Thus$, B$ is obtained by rotating $A$ in clockwise direction about origin.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The eccentricity of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is $e$ $=\sqrt{\frac{a^2+b^2}{a^2}}$.
→If A $\subset$ B and B $\subset$ C , then A $\subset$ C. If it is true, prove it. If it is false, give an example.
→The set of real numbers is represented by $R$.
→If $\tan \alpha=\frac{x}{x+1}$ and $\tan \beta=\frac{1}{2 x+1}$, then the value of $\alpha+\beta$ is $\frac{\pi}{6}$.
→The given statements is corect? Write a correct form of the given incorrect statements.
{x : x + 3 = 3} = $\phi$
→{x : x + 3 = 3} = $\phi$
$A \cup(B \cup C)=(A \cup B) \cup C$
→Determine whether the following compound statements are true or false:
Delhi is in India and 2 + 2 = 5.
Delhi is in India and 2 + 2 = 5.
Justify: Let P(n) be a statement and let P(k) ⇒ P(k + 1), for some natural number k, then P(n) is true for all n ∈ N.
The range of a series $=$ Maximum value $-$ Minimum value
→State True or False for the following:
The order relation is defined on the set of complex numbers.
The order relation is defined on the set of complex numbers.