Let be the complex number 2 3+i 2 3. Then the number of distinct complex numbers z satisfying vmatrixz+1& & ^2\ &z+ ^2&1\ ^2&1&z+ vmatrix=0 is equal to ____ . (IIT-JEE, 2010)

Question

Accepted Answer

Correct answer: 1. (1) =e^ i2 3 (z+1 ^2 z+ ^21 ^21z+ )=0 Applying ( C_1 C_1+C_2+C_3 ) ⇒z(1 ^21z+ ^2111z+ )=0 ⇒z^3=0 z=0 is only solution.

$Let ω be the complex number cos \frac{2 π}{3} + i sin \frac{2 π}{3} . Then the number of distinct complex numbers z satisfying z + 1 ω ω^{2} ω z + ω^{2} 1 ω^{2} 1 z + ω = 0 is equal to ____ . (IIT-JEE, 2010)$

Solution

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