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Simiplify : (1+ i)^(-1)...

Simiplify : `(1+ i)^(-1)`

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Verified by Experts

The correct Answer is:
`(1-i)/(2)`
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ICSE-COMPLEX NUMBERS-Exercise (B)
  1. Find the multiplicative inverse of each of the following complex numbe...

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  2. Find the multiplicative inverse of each of the following complex numbe...

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  3. Simiplify : (1+ i)^(-1)

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  4. Simiplify : sqrt(-(49)/(25)) sqrt(-(1)/(9))

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  5. Simiplify : sqrt(-64).(3 + sqrt(-361))

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  6. Simiplify : (3-7i)^(2)

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  7. Simiplify : (-(1)/(2)- (sqrt3)/(2)i)^(2)

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  8. Simiplify : ((1-i)^(3))/((1-i^(3))

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  9. Simiplify : ((1+i)/(1-i))^(4n+1) (n is a positive integer)

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  10. Simiplify : (sqrt((5+12i)) + sqrt((5-12i)))/(sqrt((5+12i))-sqrt((5-12...

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  11. Prove that [((3+2i)/(2-5i))+ ((3-2i)/(2+5i))] is rational

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  12. Show that (1+ 2i)/(3+4i) xx (1-2i)/(3-4i) is real

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  13. Perform the indicated operation and give your answer in the form x+yi,...

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  14. Perform the indicated operation and give your answer in the form x+yi,...

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  15. Perform the indicated operation and give your answer in the form x+yi,...

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  16. Perform the indicated operation and give your answer in the form x+yi,...

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  17. Perform the indicated operation and give your answer in the form x+yi,...

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  18. If x+ yi= (u+ vi)/(u-yi), prove that x^(2) + y^(2)=1

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  19. Prove that : [4 + 3 sqrt(-20)]^((1)/(2)) + [4 -3 sqrt(-20)]^((1)/(2))...

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  20. Express the following in the form a+ bi sqrt((5(2+i))/(2-i))

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