Question:
The modulus of the square root of the conjugate of $-7 + 24\sqrt{-1}$ is __________
The modulus of the square root of the conjugate of $-7 + 24\sqrt{-1}$ is __________
Show Hint
Always use $|\sqrt{z}| = \sqrt{|z|}$.
Updated On: Apr 26, 2026
- 3
- 4
- 16
- 5
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
\[ |\sqrt{z}| = \sqrt{|z|} \] Step 1: Find conjugate. \[ z = -7 + 24i \Rightarrow \bar{z} = -7 - 24i \]
Step 2: Find modulus. \[ |\bar{z}| = \sqrt{(-7)^2 + (-24)^2} = \sqrt{49 + 576} = \sqrt{625} = 25 \]
Step 3: Apply property. \[ |\sqrt{\bar{z}}| = \sqrt{25} = 5 \]
Step 4: Conclusion. Answer = 5
\[ |\sqrt{z}| = \sqrt{|z|} \] Step 1: Find conjugate. \[ z = -7 + 24i \Rightarrow \bar{z} = -7 - 24i \]
Step 2: Find modulus. \[ |\bar{z}| = \sqrt{(-7)^2 + (-24)^2} = \sqrt{49 + 576} = \sqrt{625} = 25 \]
Step 3: Apply property. \[ |\sqrt{\bar{z}}| = \sqrt{25} = 5 \]
Step 4: Conclusion. Answer = 5
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET binomial distribution Questions
- If \( X \sim B(4, p) \) and \( 2 P(X = 3) = 3 P(X = 2) \), then the value of \( p \) is:
- The volume of a tetrahedron whose vertices are \( A = (-1, 2, 3) \), \( B = (3, -2, 1) \), \( C = (2, 1, 3) \), and \( D = (-1, -2, 4) \) is
- The probability of a shooter hitting a target is \( \frac{3}{4} \). Find the probability of hitting the target exactly 4 times in 5 shots.
- In a Binomial distribution with \(n=10\) and \(p=0.4\), find the variance.
- Two cards are drawn successively with replacement from well shuffled pack of 52 cards, then the probability distribution of number of queens is
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions