Find the square root of the following complex numbers: -7+24i - Vidyadip

Question

Find the square root of the following complex numbers:
$-7+24\text{i}$

✓

Answer

Let $\text{z}=-7+24\text{i}$
$\Rightarrow|\text{z}|=\sqrt{(-7)^2+24^2}$
$=\sqrt{49+576}$
$=\sqrt{625}$
$=25$
$\therefore\sqrt{-7-24\text{i}}=\pm\Bigg\{\sqrt{\frac{25-7}{2}}+\text{i}\sqrt{\frac{25+7}{2}}\Bigg\} \ (\because\text{y}<0)$
$=\pm\Bigg\{\sqrt{\frac{18}{2}}+\text{i}\sqrt{\frac{32}{2}}\Bigg\}$
$=\pm\{\sqrt{9}+\text{i}\sqrt{16}\}$
$=\pm\{3-4\text{i}\}$

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 "3 Marks Question" 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

A man saves ₹ 32 during the first year, ₹ 36 in the second year and in this way he increases his savings by ₹ 4 every year. Find in what time his saving will be ₹ 200.

Differentiate the following function with respect to x:$\text{x}^{-4}(3-\text{4x}^{-5})$

Solve the following linear inequations in R:
$\frac{\text{x}-1}{\text{x}+3}>2$

Using binomial theorem, expand: $\left(\frac{2 x}{3}-\frac{3}{2 x}\right)^6$

One urn contains two black balls $($labelled $B_1$ and $B_2)$ and one white ball. $A$ second urn contains one black ball and two white balls $($labelled $W_1$ and $W_2).$ Suppose the following experiment is performed. One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball:

Write the sample space showing all possible outcomes.
What is the probability that two black balls are chosen?
What is the probability that two balls of opposite colour are chosen?

Prove that:
$\sin\frac{8\pi}{3}\cos\frac{23\pi}{6}+\cos\frac{13\pi}{3}\sin\frac{35\pi}{6}=\frac{1}{2}$

Find what the following equations become when the origin is shifted to the point $(1, 1)$?
$x^2 + xy − 3x − y + 2 = 0$

Which term of the sequence $12+8\text{i},\ 6\text{i},\ 10+4\text{i},\ ...$ is $(a)$ real $(b)$ purely imaginary$?$

If the points A(3, 2, -4), B(9, 8, -10) and C(5, 4, -6) are collinear, find the ratio in which C divides AB.

Prove the following by using the principle of mathematical induction for all n ∈ N:
$\Big(1+\frac{1}{1}\Big)\Big(1+\frac{1}{2}\Big)\Big(1+\frac{1}{3}\Big)...\Big(1+\frac{1}{\text{n}}\Big)=(\text{n+1}).$