arg ( 3 + i 2 - i + 3 - i 2 + i ) is equal to

MCQ

$arg\left( {\frac{{3 + i}}{{2 - i}} + \frac{{3 - i}}{{2 + i}}} \right)$ is equal to

A
$\frac{\pi }{2}$
B
$ - \frac{\pi }{2}$
✓
$0$
D
$\frac{\pi }{4}$

✓

Answer

Correct option: C.

$0$

c
(c) $arg\left( {\frac{{3 + i}}{{2 - i}} + \frac{{3 - i}}{{2 + i}}} \right) = arg\left( {\frac{{6 + 5i + {i^2} + 6 - 5i + {i^2}}}{5}} \right)$
$ = arg\left( {\frac{{10}}{5}} \right) = 0$.

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 "M.C.Q (1 Marks)" from STD 11 - 4.1 complex nubers→STD 11 - 4.1 complex nubers — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

One coin is tossed once. Find the probability of getting $A$ tail.

→

Let $a , r , s , t$ be nonzero real numbers. Let $P \left( at ^2\right.$, $2$at), $Q , R \left( ar ^2\right.$, 2ar) and $\left( as ^2\right.$, 2as) be distinct points on the parabola $y^2=4 a x$. Suppose that $P Q$ is the focal chord and lines $Q R$ and $P K$ are parallel, where $K$ is the point $(2 a , 0)$

$1.$ The value of $r$ is

$(A)$ $-\frac{1}{t}$ $(B)$ $\frac{t^2+1}{t}$ $(C)$ $\frac{1}{ t }$ $(D)$ $\frac{t^2-1}{t}$

$2.$ If st $=1$, then the tangent at $P$ and the normal at $S$ to the parabola meet at a point whose ordinate is

$(A)$ $\frac{\left(t^2+1\right)^2}{2 t^3}$ $(B)$ $\frac{a\left(t^2+1\right)^2}{2 t^3}$ $(C)$ $\frac{a\left(t^2+1\right)^2}{t^3}$ $(D)$ $\frac{a\left(t^2+2\right)^2}{t^3}$

Give the answer question $1$ and $2.$

→

Let $C$ be the circle with centre at $(1, 1)$ and radius $= 1$. If $T$ is the circle centred at $(0, y),$ passing through origin and touching the circle $C$ externally, then the radius of $T$ is equal

→

The plane $ax + by + cz + (-3) = 0$ meet the co$-$ordinate axes in $\text{A, B, C.}$ Then centroid of the triangle is:

→

If $A =\{a, b, c\}$, then the numbers of all possible non - empty relation on A is :

→

If $P$ is a point such that the ratio of the squares of the lengths of the tangents from $P$ to the circles${x^2} + {y^2} + 2x - 4y - 20 = 0$ and ${x^2} + {y^2} - 4x + 2y - 44 = 0$ is $2 : 3$, then the locus of $P$ is a circle with centre

→

Eight straight lines are drawn in the plane such that no two lines are parallel and no three lines are concurrent.The number of parts into which these lines divide the plane, is:

→