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If z^2+z|z|+|z^2|=0, then the locus z is...

If `z^2+z|z|+|z^2|=0,` then the locus `z` is a. a circle b. a straight line c. a pair of straight line d. none of these

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Express the following complex numbers in a+i b form: ((3-2i)(2+3i))/((...

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  2. If a ,b ,c are nonzero real numbers and a z^2+b z+c+i=0 has purely i...

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  3. If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight ...

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  4. If the sum of the roots of the equation 1/(x+a)+1/(x+b)=1//c is zero,...

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  5. Solve the equation x^2+p x+45=0. it is given that the squared differen...

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  6. Find the least positive integer n such that ((2i)/(1+i))^n is a positi...

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  7. z1a n dz2 lie on a circle with center at the origin. The point of inte...

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  8. If alpha,beta are the roots of the equation 2x^2-35x+2=0 , the find ...

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  9. If one root of the equation z^2-a z+a-1= 0 is (1+i), where a i...

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  10. If |z1|=|z2|=|z3|=1 and z1+z2+z3=0 then the area of the triangle whose...

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  11. Simplify: (sqrt(5+12 i)+sqrt(5-12 i))/(sqrt(5+12 i)-sqrt(5-12 i))

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  12. Find a quadratic equation whose product of roots x1 and x2 is equa...

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  13. If sqrt(5-12 i)+sqrt(-5-12 i)=z , then principal value of a rgz can be

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  14. If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,y=pdot

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  15. If a and b(!=0) are the roots of the equation x^2+a x+b=0, then find...

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  16. Let A ,B ,C ,D be four concyclic points in order in which A D : A B=C ...

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  17. Convert (1+3i)/(1-2i) into the polar form.

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  18. If the sum of the roots of the equation (a+1)x^2+(2a+3)x+(3a+4)=0 is ...

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  19. Let the altitudes from the vertices A, B and Cof the triangle e ABCmee...

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  20. For |z-1|=1, show that tan{[a r g(z-1)]/2}-((2i)/z)=-i

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