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If a+ib = sqrt((1+i)/(1-i)), prove that ...

If a+ib = `sqrt((1+i)/(1-i))`, prove that `a^2+b^2=1`

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A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. If x=(1+i)/sqrt2.Prove that x^6+x^4+x^2+1=0

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  2. Prove that abs((1+i)/(1-i)) = 1

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  3. If a+ib = sqrt((1+i)/(1-i)), prove that a^2+b^2=1

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  4. Prove that abs(costheta-isintheta) = 1

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  5. If (costheta-isintheta)^2 = x -iy, show that x^2+y^2 = 1

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  6. Complete the following table

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  7. When two complex numbers are equal? Find the real values of x and y fo...

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  8. Match the following

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  9. Fill in the blanks by choosing the correct answer from the bracket ove...

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  10. Suppose z1 = 1 - i and z2 = -2 + 4i Find z1z2

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  11. Suppose z1 = 1 - i and z2 = -2 + 4i Find overlinez1

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  12. Suppose z1 = 1 - i and z2 = -2 + 4i Find Im ((z1z2)/z1) and Re ((z1z2...

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  13. Suppose z1 = 1 - i and z2 = -2 + 4i Joseph evaluted abs((z1z2)/z1) usi...

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  14. Suppose z = x + iy and w = (1-iz)/(z-i) Find 1 - iz and z - 1 in the s...

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  15. Suppose z = x + iy and w = (1-iz)/(z-i) Find absw. If absw = 1, prove...

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  16. Consider the complex number z1 = 2 - i and z2 = -2 + i Find (z1z2)/z1...

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  17. Consider the complex number z1 = 2 - i and z1 = -2 + i Raju prove tha...

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  18. Consider the complex number z1 = 2 - i and z2 = 2 + i Find 1/(z1z2). ...

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  19. Given that for any complex number z, absz^2 = zoverlinez . Prove that ...

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  20. Given that for any complex number z, absz^2 = zoverlinez . Prove that ...

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