Download App

4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
If $arg\,z < 0$ then $arg\,( - z) - arg\,(z)$ is equal to
  • ✓
    $\pi $
  • B
    $ - \pi $
  • C
    $ - \frac{\pi }{2}$
  • D
    $\frac{\pi }{2}$
✓

Answer

Correct option: A.
$\pi $
a
(a) Since arg $z < 0$ i.e. -ve, we choose $arg\ z = -\theta$
where $\theta $ is $+ve$
$arg\  ( - z) = - [ + \pi - ( - \theta )]$
$ = - \pi - \theta = 2\pi + ( - \pi - \theta ) = \pi + arg(z)$
$ \Rightarrow \,arg\,( - z) - arg(z) = \pi .$

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

Explore more

More "MCQ" from 4.1 complex nubers→4.1 complex nubers — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If n is a positive integer and ${C_k} = {\,^n}{C_k}$, then the value of ${\sum\limits_{k = 1}^n {{k^3}\left( {\frac{{{C_k}}}{{{C_{k - 1}}}}} \right)} ^2}$ =
→
For all $n \geq 2, n n^2\left(n^4>1\right)$ is divisible by:
→
The sum of the coefficients of all the even powers of $x$ in the expansion of $\left(2 x^2-3 x+1\right)^{11}$ is:
 
→
Let $\mathrm{P}$ be a parabola with vertex $(2,3)$ and directrix $2 x+y=6$. Let an ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ of eccentricity $\frac{1}{\sqrt{2}}$ pass through the focus of the parabola $\mathrm{P}$. Then the square of the length of the latus rectum of $\mathrm{E}$, is
→
Number of value/s of $x$ satisfy given eqution ${5^{x - 1}} + 5.{(0.2)^{x - 2}} = 26$.
→
Let $P\left(x_1, y_1\right)$ and $Q\left(x_2, y_2\right), y_1<0, y_2<0$, be the end points of the latus rectum of the ellipse $x^2+4 y^2=4$. The equations of parabolas with latus rectum $P Q$ are

$(A)$ $x^2+2 \sqrt{3} y=3+\sqrt{3}$

$(B)$ $x^2-2 \sqrt{3} y=3+\sqrt{3}$

$(C)$ $x^2+2 \sqrt{3} y=3-\sqrt{3}$

$(D)$ $x^2-2 \sqrt{3} y=3-\sqrt{3}$

→
If $\left(\frac{3^{6}}{4^{4}}\right) \mathrm{k}$ is the term, independent of $\mathrm{x}$, in the binomial expansion of $\left(\frac{\mathrm{x}}{4}-\frac{12}{\mathrm{x}^{2}}\right)^{12}$, then $\mathrm{k}$ is equal to ...... .
→
If $\log _{3} 2, \log _{3}\left(2^{x}-5\right), \log _{3}\left(2^{x}-\frac{7}{2}\right)$ are in an arithmetic progression, then the value of $x$ is equal to $.....$
→
The value of $\sin {47^o} + \sin 61^\circ - \sin 11^\circ - \sin 25^\circ = $
→
For $x \in R$, then number of real roots of the equation $3 x^2-4\left|x^2-1\right|+x-1=0$ is. . . . . .
→