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If omega is the complex cube root of uni...

If `omega` is the complex cube root of unity then ` |[1,1+i+omega^2,omega^2],[1-i,-1,omega^2-1],[-i,-i+omega-1,-1]|=`

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CENGAGE ENGLISH-DETERMINANTS-All Questions
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  2. Let omega be the complex number cos((2pi)/3)+isin((2pi)/3). Then the...

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  3. If omega is the complex cube root of unity then |[1,1+i+omega^2,omeg...

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  4. Consider the determinant Delta=|[a1+b1x^2,a1x^2+b1,c1],[a2+b2x^2,a2x^2...

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  5. If a x1^2+b y1^2+c z1^2=a x2 ^2+b y2 ^2+c z2 ^2=a x3 ^2+b y3 ^2+c z3 ^...

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  6. If A , B ,a n dC are the angles of triangle, show that the system of...

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  7. Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...

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  11. Prove that =|[a,c,c-a,a+c],[c,b,b-c,b+c],[a-b,b-c,0,a-c],[x,y,z,1+x+y]...

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  13. Absolute value of sum of roots of the equation |[x+2,2x+3, 3x+4],[ 2x+...

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  14. Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...

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  15. The product of all values of t , for which the system of equations (a-...

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  16. " if " a(1) ,a(2), a(3)….." are in A.P, then find the value of the fo...

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  17. Let omega=-1/2+i(sqrt(3))/2. Then the value of the determinant |(1,1,1...

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  18. Factorize: a x+b x+a y+b y a x^2+b y^2+b x^2+a y^2 a^2+b c+a b+a...

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  19. If g(x)=|[a^(-x),e^(x loge a),x^2],[a^(-3x),e^(3x loge a),x^4],[a^(-5x...

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  20. The sum of values of p for which the equations x+y+z=1, x+2y +4z...

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