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Evaluate the following: \ (i^(77)+i^(70)...

Evaluate the following: `\ (i^(77)+i^(70)+i^8+i^(414))^3`

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The correct Answer is:
-8
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CBSE COMPLEMENTARY MATERIAL-COMPLEX NUMBERS AND QUADRATIC EQUATIONS -Short Answer Type Questions
  1. Evaluate : sqrt(-16) + 3 sqrt(-25) + sqrt(-36) - sqrt(-625).

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  2. Evaluate: (ii) isqrt-16+isqrt-25+sqrt49-isqrt-49+14

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  3. Evaluate the following: \ (i^(77)+i^(70)+i^8+i^(414))^3

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  4. Evaluate: (iv) ((3+sqrt5i)(3-sqrt5i))/((sqrt3+sqrt2i)-(sqrt3-sqrt2i))

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  5. Find the real values of x\ a n d\ y ,\ if:(x+i y)(2-3i)=4+i

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  6. If n is any positive integer, write the value of (i^(4n+1)-i^(4n-1))/2...

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  7. If z1=sqrt2 (cos 30^(@) +isin60^(@)),z2=sqrt3 (cos 60^(@) +isin30^(@))...

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  8. If |z+4|lt=3 then find the greatest and least values of |z+1|dot

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  9. Find the real value of a for which 3i^3-2a i^2+(1-a)i+5 is real.

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  10. If arg(z-1)=arg(z+3i), then find (x-1):y, where z=x+iy.

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  11. If z= x+iy and the amplitude of (z-2-3i) is (pi)/(4). Find the relatio...

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  12. If x+i y=sqrt((1+i)/(1-i)), prove that x^2+y^2=1.

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  13. The real value of theta for which the expression (1+icostheta)/(1-2ic...

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  14. If |(z-5i)/(z+5i)|=1 show that z is a real number

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  15. If xn =cos ((pi)/(2^(n)))+isin((pi)/(2^(n)))Prove that x1 x2…..xoo=-1

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  16. Find the real value of x and y if ((1+i)x-2i)/(3+i)+((2-3i)y+i)/(3-i)...

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  17. If (1+i)(1+2i)(1+3i)(1+n i)=(x+i y) , show tht 2. 5. 10 (1+n^2)=x^2+y^...

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  18. If z=2-3i show that z^2=4z+13=0 and hence find the value of 4z^3-3z^2+...

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  19. If ((1+i)/(1-i))^3-((1-i)/(1+i))^3 =a+ib find a and b

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  20. For complex numbers z1 = 6+3i, z2=3-I find (z1)/(z2)

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