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Show that : (i) {i^(19) + (1/i)^(25)}^...

Show that :
(i) `{i^(19) + (1/i)^(25)}^(2) = -4 " "(ii) {i^(17) - (1/i)^(34)}^(2) = 2i`
(iii) `{i^(18) + (1/i)^(24)}^(3) = 0 " " (iv) i^n + i^(n+1) + i^(n +2) + i^(n + 3) = 0`, for all `n in N`.

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Verified by Experts

The correct Answer is:
(i) - -4, (ii) - 2i, (iii) - 0, (iv) - 0
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FULL MARKS-COMPLEX NUMBERS -ADDITIONAL QUESTIONS SOLVED
  1. Evaluate the following: (i) i^(135) " "(ii) i^(19) " " (iii) i^(...

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  2. Show that : (i) {i^(19) + (1/i)^(25)}^(2) = -4 " "(ii) {i^(17) -...

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  3. The value of sum(i=1)^(13) (n^(n) + i^(n-1)) is

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  4. Find the real values of x and y, if (3x - 7) + 2 iy = -5y + (5 + x)...

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  5. For what values of x and y the numbers -3+ix^(2)y and x^(2)+y+4i and c...

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  6. Given x = 2 - 3i and y = 4 + i. Find (i) xy " "(ii) x + y " ...

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  7. If z1 = 4 - 7i , z2 = 2 + 3i and z3 = 1 + i show that z1 + (z2 + z3...

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  8. Given z1 = 1 + i, z2 = 4 - 3i and z3 = 2 + 5i verify that. z1(z2 - z...

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  9. Given z1 = 4 - 7i and z2 = 5 + 6i find the additive and multiplicative...

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  10. Express the following in the standard form a + ib. (2(i -3))/((1 + ...

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  11. Find the least positive integer n such that ((1 + i)/(1 - i))^(n) = 1.

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  12. Find x and y for which of the following is satisfied. ((1+i)x-2i)/(3...

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  13. Find the modulus and argument of the following complex numbers and con...

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  14. Find the square roots of -15 - 8i

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  15. Express the following in the standard form a + ib. (i^4 + i^9 + i^(16)...

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  16. Find the modulus or the absolute value of ((1 + 3i)(1 - 2i))/((3 + 4i)...

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

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  18. Show that the points represented by the complex numbers 7+9i, -3+7i, 3...

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  19. Find the square root of (-7 + 24i).

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  20. If the imaginary part of (2z + 1)/(iz + 1) is -2, then show that the l...

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