Question:
Let $z=x+iy$ be a complex number, where $i=\sqrt{-1}$ is the complex unit. Then $|z-1+i|=5$ is a circle with:
Let $z=x+iy$ be a complex number, where $i=\sqrt{-1}$ is the complex unit. Then $|z-1+i|=5$ is a circle with:
Show Hint
Always factor out a negative sign to identify the centre $z_0$ correctly.
Updated On: Apr 28, 2026
- centre at (-1,1) and radius 5
- centre at (1,1) and radius $\sqrt{5}$
- centre at (-1,-1) and radius $\sqrt{5}$
- centre at (1,1) and radius 25
- centre at (1,-1) and radius 5
Show Solution
Verified By Collegedunia
The Correct Option is
Solution and Explanation
Step 1: Concept
The equation $|z - z_0| = r$ represents a circle with centre $z_0$ and radius $r$.
Step 2: Analysis
Rewrite $|z - 1 + i| = 5$ as $|z - (1 - i)| = 5$.
Step 3: Conclusion
The centre is $z_0 = 1 - i$, which corresponds to the point $(1, -1)$, and the radius is 5. Final Answer: (E)
The equation $|z - z_0| = r$ represents a circle with centre $z_0$ and radius $r$.
Step 2: Analysis
Rewrite $|z - 1 + i| = 5$ as $|z - (1 - i)| = 5$.
Step 3: Conclusion
The centre is $z_0 = 1 - i$, which corresponds to the point $(1, -1)$, and the radius is 5. Final Answer: (E)
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Complex numbers Questions
- The principal argument of the complex numb $Z=\frac{1+\sin \frac{\pi}{3}+i \cos\frac{\pi}{3} }{1+\sin \frac{\pi}{3} - i \cos\frac{\pi}{3} }$ is
- If $ \sqrt{x+iy}=\pm (a+ib), $ then $ \sqrt{-x-iy} $ is equal to
- If $a = e^{i \theta}$ , then $\frac{1 + a}{1-a}$ is equal to
- If the conjugate of a complex number $z$ is $\frac{1}{i - 1}$ , then $z$ is
- The sum of odd integers from $1$ to $2001$ is
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions