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For any two complex numbers z1 and z2 pr...

For any two complex numbers `z_1` and `z_2` prove that
`Re(z_1z_2) = Re(z_1)Re(z_2) - Im(z_1)Im(z_2)`

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A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Solve: x^2+x/sqrt3+1=0

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  2. Evaluate [i^18+(1/i)^25]^3

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  3. For any two complex numbers z1 and z2 prove that Re(z1z2) = Re(z1)Re(...

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  4. Reduce (1/(1-4i) - 2/(1+i)) ((3-4i)/(5+i)) to the standard form

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  5. If x-iy=sqrt((a-ib)/(c-id), prove that (x^2+y^2)^2 = (a^2+b^2)/(c^2+d^...

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  6. Convert the following in to the polar form (1+7i)/(2-i)^2

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  7. Consider the complex number z=(1+3i)/(1-2i).Write z in polar form.

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  8. Solve the following equations 3x^2-4x+20/3=0

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  9. Solve the following equations x^2-2x+3/2=0

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  10. Solve the following equations 27x^2-10x+1=0

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  11. Solve the equation 21x^2-28x+10=0

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  12. If z1=2-i,z2=1+i Hence find abs[(z1+z2+1)/(z1-z2+i)]

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  13. If a+ib=(x+i)^2/(2x^2+1), prove that a^2+b^2=(x^2+1)^2/(2x^2+1)^2

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  14. Let z1=2-i, z2=-2+i. Find Re((z1z2)/overlinez1)

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  15. Let z1=2-i, z2=-2+i. Find Im (1/(z1overlinez1))

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  16. Find the modulus and argument of the complex number (1+2i)/(1-3i)

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  17. Find the real numbers x and y if (x-iy)(3+5i) is the conjugate of - 6 ...

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  18. Find the modulus of (1+i)/(1-i) - (1-i)/(1+i)

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  19. If (x+iy)^3 = u + iv, then show that u/x+v/y=4(x^2-y^2)

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  20. If alpha and beta are different complex numbers with absbeta = 1, then...

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