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If (a+i)^2/(2a-i) = p+iq, prove that p^2...

If `(a+i)^2/(2a-i) = p+iq`, prove that `p^2+q^2 = (a^2+1)^2/(4a^2+1)`

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A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Consider the complex number z1 = 3+i and z2 = 1+i .Using the value of ...

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  2. Prove that abs((a+i)^2/(2a-i)) = (a^2+1)/(sqrt(4a^2+1))

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  3. If (a+i)^2/(2a-i) = p+iq, prove that p^2+q^2 = (a^2+1)^2/(4a^2+1)

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  4. If x=(1+i)/sqrt2, prove that x^2 = i

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  5. If x=(1+i)/sqrt2.Prove that x^6+x^4+x^2+1=0

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

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

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

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

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  10. Complete the following table

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

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  12. Match the following

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

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

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

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

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

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

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

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

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