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Express the following complex numbers in...

Express the following complex numbers in the polar form : `2 + sqrt(3) i`

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FULL MARKS-COMPLEX NUMBERS -ADDITIONAL QUESTIONS SOLVED
  1. Find the modulus and principal argument of (1 + i) and hence express i...

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  2. Express the following complex numbers in the polar form. (i) (1 + i)...

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  3. Express the following complex numbers in the polar form : 2 + sqrt(3) ...

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  4. Find the modulus and principal argument of the following complex numbe...

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  5. Express the following complex numbers in the polar form : -1 - i

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  6. Express the following complex numbers in the polar form : 1 - i

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  7. Evaluate i^(50)

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  8. Evaluate i^(59)

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  9. Prove that : (1 + i)^(4n) and (1 + i)^(4n + 2) are real and purely ima...

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  10. If x = cos alpha + i sin alpha , y = cos beta + i sin beta, prove that...

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  11. If a = cos 2alpha + i sin 2 alpha, b = cos 2 beta + i sin 2 beta and c...

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  12. Solve : x^4 + 4 = 0

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  13. If x = a + b, y = a omega + b omega^2, z = aomega^2 + b omega, show th...

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  14. ((1 - i)/(1+ i))^(100) = a + ib then (a,b) is ……….

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  15. If ((1 + i)/(1 - i))^(3) - ((1 - i)/(1 + i))^(3) = x + iy then (x, y) ...

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  16. Evaluate i^(60)

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  17. Fill in the blanks of the following : For any two complex numbers z1...

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  18. Multiplicative inverse of 1 + i is ………..

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  19. arg(z) + arg(barz) (z != 0) is ………..

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  20. If |z| = 4 and arg(z) = (5pi)/6, then z = …………..

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