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If z =frac((1+i)(1+sqrt3i)^2)(1-i) , fin...

If z =`frac((1+i)(1+sqrt3i)^2)(1-i)` , find |z| , arg z and `barz` .

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. Find the square root of x^2/y^2+y^2/x^2+1/(2i)(x/y+y/x)+31/16 .

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  2. Find the conjugate, modulus and argumetn of sqrt(2-)sqrt(2i)

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  3. If z =frac((1+i)(1+sqrt3i)^2)(1-i) , find |z| , arg z and barz .

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  4. Write 1+i/2-i in the trigonometrical form.

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  5. If z1= 3i and z2 = -1 -i , find the value of arg z1/z2 .

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  6. Find the modulus and amplitude of frac1((1-i)^2)-frac1((1+i)^2) . Als...

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  7. Solve the equation z^2 +|z|=0 , where z is a complex number.

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  8. Find the complex number z if z^2+barz=0

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  9. Solve for z: z^2 = (ibarz)^2 .

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  10. which of the foolowing satisfies |z+1|=z+2+2i

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  11. Determine the complex numbers which satisfy the equation -ibarz=z^2.

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  12. Find all complex numbers satisfying |z|^2+z^2-5+isqrt3 = 0.

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  13. Is there any z such that |(z+2)/(z+4i)|= 1 ? If so, find z.

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  14. IF 1age1, find all complex numbers z satisfying the equatioin z+a|z+|+...

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  15. Find all complex numbers satisfying barz= z^2 .

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  16. For every real number c ge 0, find all complex numbers z which satisfy...

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  17. Let the complex numbers z of the form x+iy satisfy arg ((3z-6-3i)/(2z-...

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  18. If z = x + iy and |z+6| = |2z+3| , prove that x^2+y^2=9.

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  19. if argument of (z-1)/(z+1)=pi/4 then prove that x^2+y^2-2y=1

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  20. If z is a normal complex for which |z| = 1 , prove thatfrac (z-1)(z+1...

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