Fill in the Blanks
Number of solutions of the equation z2 + |z|2 = 0 is ______.
Number of solutions of the equation z2 + |z|2 = 0 is infinitely many.
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.
Concept: Algebraic Operations of Complex Numbers
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