Question:medium
Let \( z \) be a complex number such that \( |z-6|=5 \) and \( |z+2-6i|=5 \). Then the value of
\( z^3+3z^2-15z+14 \) is equal to:
Let \( z \) be a complex number such that \( |z-6|=5 \) and \( |z+2-6i|=5 \). Then the value of
\( z^3+3z^2-15z+14 \) is equal to:
Show Hint
When two circles with equal radii touch externally, the common point lies exactly at the midpoint of their centers.
Updated On: Mar 5, 2026
- \(37\)
- \(42\)
- \(50\)
- \(61\)
Show Solution
The Correct Option is A
Solution and Explanation
Was this answer helpful?
1
Top Questions on Complex numbers
- Let $z$ be the complex number satisfying $|z - 5| \le 3$ and having maximum positive principal argument. Then $34 \left| \frac{5z - 12}{5iz + 16} \right|^2$ is equal to :
- JEE Main - 2026
- Mathematics
- Complex numbers
- If \(x^2+x+1=0\), then the value of \(\left(x + \frac{1}{x}\right)^2 + \left(x^2 + \frac{1}{x^2}\right)^2 + \left(x^3 + \frac{1}{x^3}\right)^2 + \dots + \left(x^{25} + \frac{1}{x^{25}}\right)^2\) is:
- JEE Main - 2026
- Mathematics
- Complex numbers
- Let \[ S = \{ z \in \mathbb{C} : 4z^2 + \bar{z} = 0 \}. \] Then \[ \sum_{z \in S} |z|^2 \] is equal to
- JEE Main - 2026
- Mathematics
- Complex numbers
- $z$ is a complex number satisfying \[ \left| \frac{z - 6i}{z - 2i} \right| = 1 \quad \text{and} \quad \left| \frac{z - 8 + 2i}{z + 2i} \right| = \frac{3}{5} \] then find $\sum |z|^2$.
- JEE Main - 2026
- Mathematics
- Complex numbers
- Want to practice more? Try solving extra ecology questions todayView All Questions
Questions Asked in JEE Main exam
In an equilateral prism the path of a ray is shown in the figure. Determine the refractive index of the prism.
- JEE Main - 2026
- Ray optics and optical instruments
