Question

Number of solutions of the equation z² + |z|² = 0 is ______.

Options

• 1

• 2

• 3

• Infinitely many

Answer 1

Number of solutions of the equation z² + |z|² = 0 is infinitely many.

Explanation:

z² + |z|² = 0, z ≠ 0

⇒ x² – y² + i2xy + x² + y² = 0

⇒ 2x² + i2xy = 0, 2x(x + iy) = 0

⇒ x = 0 or x + iy = 0  ......(not possible)

Therefore, x = 0 and z ≠ 0

So y can have any real value. Hence infinitely many solutions.