Complex Numbers and Quadratic Equations · Class 11 · CBSE · Science Mathematics
Find the square roots of the complex number -7 + 24i.
Practice question from Complex Numbers and Quadratic Equations (Class 11 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
hard · Subjective · Q-3ECBBD
Find the square roots of the complex number -7 + 24i.
Answer: The square roots of -7 + 24i are 3 + 4i and -3 - 4i. Let (a + bi)² = -7 + 24i; then a² - b² = -7 and 2ab = 24. Since a² + b² = √((-7)² + 24²) = 25, we get a² = 9 and b² = 16; choosing signs so that ab = 12 gives the roots ±(3 + 4i).
Solution
Let the square root be . Comparing real and imaginary parts gives and . Also, , so and . Since , the roots are and .
More from Complex Numbers and Quadratic Equations
- If z = 3 - 4i, where i² = -1, then the modulus of z is
- The roots of the quadratic equation x² + 4x + 13 = 0 are
- The value of (1 + i)/(1 - i), where i² = -1, is
- If z = 2 - 3i, where i² = -1, then z multiplied by its conjugate is
Practise more Mathematics
Sign up free for adaptive practice on this chapter, with instant feedback and hints on every question.
Start practising freeFree to start · No credit card needed