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P(z1),Q(z2),R(z3)a n dS(z4) are four com...

`P(z_1),Q(z_2),R(z_3)a n dS(z_4)` are four complex numbers representing the vertices of a rhombus taken in order on the complex lane, then which one of the following is/ are correct? `(z_1-z_4)/(z_2-z_3)` is purely real `a m p(z_1-z_4)/(z_2-z_3)=a m p(z_2-z_4)/(z_3-z_4)` `(z_1-z_3)/(z_2-z_4)` is purely imaginary It is not necessary that `|z_1-z_3|!=|z_2-z_4|`

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  2. Find the complex number z satisfying R e(z^2) =0,|z|=sqrt(3.)

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  3. P(z1),Q(z2),R(z3)a n dS(z4) are four complex numbers representing the ...

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  4. Given that the expression 2x^3+3p x^2-4x+p has a remainder of 5 when d...

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  5. z1a n dz2 are two distinct points in an Argand plane. If a|z1|=b|z2|(w...

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  6. Consider two complex numbers alpha and beta as alpha=[(a+b i)//(a-b i)...

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  7. In how many points the graph of f(x)=x^3+2x^2+3x+4 meets the x-axis ...

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  8. If x^2+x+1=0 then the value of (x+1/x)^2+(x^2+1/(x^2))^2+...+(x^27+1/(...

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  9. If (a+ib)(c+id)(e+if)(g+ih)=A+iB, then show that (a^2+b^2)(c^2+d^2)(e^...

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  10. Find the roots of the equation x+1/x=3

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  11. Solve the equation |z|=z+1+2idot

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  12. If z=i^(i^(i)) where i=sqrt-1 then find the value of |z|

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  13. Find the values of a for which the roots of the equation x^2+a^2=8x+6...

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  14. If alpha and beta are different complex numbers with absbeta=1. then f...

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  15. If z=i log(2-sqrt3), then cosz= a. -1 b. (-1)/2 c. ...

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  16. If f(x)=x^3-x^2+a x+b is divisible by x^2-x , then find the value of...

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  17. z=x+iy and w=(1-iz)/(1+iz) and |w|=1 ,prove that z is purely real

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  18. If the equation z^4+a1z^3+a2z^2+a3z+a4=0 where a1,a2,a3,a4 are real co...

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  19. If f(x)=x^3-3x^2+2x+a is divisible by x-1, then find the remainder whe...

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  20. If z1a n dz2 are two complex numbers and c >0 , then prove that |z1+z2...

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