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Evaluate the following: i^(49)+i^(68)+i^...

Evaluate the following: `i^(49)+i^(68)+i^(89)+i^(110)`

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Given `i^(49)+i^(68)+i^(89)+i^(110)`
`=>{( i^(4))^(12)*i }+{( i^(4))^(17) }+{( i^(4))^(22)*i }+{( i^(4))^(27)*i^2 }`
As `i^4=1`
So `i+1+i+i^2`
`2i+1-1`
as `i^2=-1`
...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. Evaluate the following: \ (i^(77)+i^(70)+i^87+i^(414))^3

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  2. Evaluate the following: i^(30)+i^(40)+i^(60)

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  3. Evaluate the following: i^(49)+i^(68)+i^(89)+i^(110)

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  4. Compute the following: sqrt(-144)

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  5. Compute the following: sqrt(-4)xxsqrt((-9)/4)

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  6. Compute the following: sqrt(-25)+3sqrt(-4)+2sqrt(-9)

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  7. A student writes the formula sqrt(a b)=sqrt(a)\ sqrt(b)dot Then he sub...

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  8. Is the following computation correct? If not give the correct comput...

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  9. If (a+b)-i(3a+2b)=5+2i, find a\ a n d\ b.

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  10. Find the multiplicative inverse of z=3-2idot

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  11. Express the following in the form a+i b : (-5i)(1/8i)

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  12. Express the following in the form a+i b :(5i)(-3/5i)

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  13. Express the following in the form a+i b : i^(-39)

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  14. Express the following in the form a+i b :(-i)(2i)(-1/8i)^3

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  15. Express the following in the form a+i b : i^9+i^(19)

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  16. Express the following in the form a+i b :(1-i)^4

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  17. Express each of the following in the form a+i b :3(7+7i)+i(7+7i)

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  18. Express each of the following in the form a+i b :(1/5+2/5i)-(4+5/2i)

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  19. Express each of the following in the form a+i b :(1-i)-(-1+6i)

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  20. Express each of the following in the form a+i b :{(1/3+7/3i)+(4+1/3i)}...

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