(-3+i) ^ 53 where i ^ 2 =-1 is equal to [AMU 2000] - Vidyadip

MCQ

${{(-\sqrt{3}+i)}^{53}}$ where ${{i}^{2}}=-1$ is equal to [AMU 2000]

A
${{2}^{53}}(\sqrt{3}+2i)$
B
${{2}^{52}}(\sqrt{3}-i)$
✓
${{2}^{53}}\,\left( \frac{\sqrt{3}}{2}+\frac{1}{2}i \right)$
D
${{2}^{53}}(\sqrt{3}-i)$

✓

Answer

Correct option: C.

${{2}^{53}}\,\left( \frac{\sqrt{3}}{2}+\frac{1}{2}i \right)$

C

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 Complex Numbers→Complex Numbers — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The value of $2 \sin \left(12^{\circ}\right)-\sin \left(72^{\circ}\right)$ is

Period of $|2\sin 3\theta + 4\cos 3\theta |$ is

Let $S$ be the set of all $a \in N$ such that the area of the triangle formed by the tangent at the point $P ( b , c ), b , c \in N$, on the parabola $y ^2=2 ax$ and the lines $x=b, y=0$ is $16$ unit $^2$, then $\sum_{\text {aes }} a$ is equal to $..........$.

Equation of vertical line to the right of $y-$axis at $5$ units from $y-$axis is:

For a frequency distribution $7^{th}$ decile is computed by the formula

Coefficients of ${x^r}[0 \le r \le (n - 1)]$ in the expansion of ${(x + 3)^{n - 1}} + {(x + 3)^{n - 2}}(x + 2)$$ + {(x + 3)^{n - 3}}{(x + 2)^2} + ... + {(x + 2)^{n - 1}}$

The largest term in the expansion of ${(3 + 2x)^{50}}$ where $x = \frac{1}{5}$ is

Let $P(n): “2n < (1 \times 2 \times 3 \times ... \times n)”.$ Then the smallest positive integer for which $P(n)$ is true is:

If slope of a line is $4$ and $y-$intercept made by the line is $2$ then the equation of line will be:

The locus of a point which divides the join of $A( - 1,\;1)$ and a variable point $P$ on the circle ${x^2} + {y^2} = 4$ in the ratio $3 : 2$, is