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Show that if iz^3+z^2-z+i=0, then |z|=1...

Show that if `iz^3+z^2-z+i=0`, then `|z|=1`

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Intercept made by the circle zbar z +bar a+abar z+r=0 on the real a...

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  2. The graph of the quadratic trinomial u=a x^2+b x+c has its vertex at (...

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  3. Show that if iz^3+z^2-z+i=0, then |z|=1

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  4. Show that the equation of a circle passing through the origin and ha...

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  5. The function f(x)=a x^2+b x^2+c x+d has three positive roots. If the ...

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  6. Let z1=10+6i and z2=4+6idot If z is any complex number such that the a...

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  7. Let vertices of an acute-angled triangle are A(z1),B(z2),a n dC(z3)dot...

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  8. If (18 x^2+12 x+4)^n=a0+a(1x)+a2x2++a(2n)x^(2n), prove that ar=2^n3^r(...

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  9. If z=z0+A( bar z -( bar z 0)), w h e r eA is a constant, then prove t...

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  10. If (sinalpha)x^2-2x+bgeq2 for all real values of xlt=1a n dalpha in (0...

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  11. If z1, z2, z3 are three complex numbers such that 5z1-13 z2+8z3=0, t...

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  12. If one root x^2-x-k=0 is square of the other, then k= a.2+-sqrt(5)...

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  13. If 2z1//3z2 is a purely imaginary number, then find the value of "|"(z...

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  14. If alpha,a n dbeta be t roots of the equation x^2+p x-1//2p^2=0,w h e ...

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  15. If z1, z2, z3 are complex numbers such that (2//z1)=(1//z2)+(1//z3), t...

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  16. Find the range of (a) f(x) = (x^(2)+34 x - 71)/(x^(2) + 2x - 7) (b...

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  17. If ((3-z1)/(2-z1))((2-z2)/(3-z2))=k(k >0) , then prove that points A(z...

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  18. x^2-x y+y^2-4x-4y+16=0 represents a. a point b. a circle c. a pair...

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  19. If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

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  20. If alpha,beta are the nonzero roots of a x^2+b x+c=0 and alpha^2,beta...

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