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1+i^2+i^4+i^6+i^8++i^(20)...

`1+i^2+i^4+i^6+i^8++i^(20)`

A

Purely real complex number

B

forth quadrant

C

First quadrant

D

`2(cos(pi)/(6)+isin(pi)/(6))`

Text Solution

Verified by Experts

The correct Answer is:
Purely real complex number
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Find the values of following expressions: i^(49)+i^(68)+i^(89)+i^(110) (ii) i^(30)+i^(80)+i^(120) (iii) i^+i^2+i^3+i^4 (iv) i^5+i^(10)+i^(15) (v) (i^(592)+i^(590)+i^(586)+i^(584))/(i^(582)+i^(580)+i^(576)+i^(574)) (vi) 1+i^2+i^4+i^6+i^8+doti^(20) (vii) (1+i)^6+(1-i)^3

If (1+i^2 +i^4 +i^6 +i^208)=a +ib ,then the value of (a,b) is

Find the value of ( i^2 + i^4 + i^6 + i^7 ) / ( 1 + i^2 + i^3 ) is ( a ) 1 - i ( b ) 1 + i ( c ) 2 - i ( d ) 2 + i

1 + i^(2) + i^(4) + i^(6) = 0 .

Find the value of i^4 + i^5 + i^6 + i^7

Find the value of : i^4 + i^5 + i^6 + i^7

CBSE COMPLEMENTARY MATERIAL-COMPLEX NUMBERS AND QUADRATIC EQUATIONS -Short Answer Type Questions
  1. 1+i^2+i^4+i^6+i^8++i^(20)

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  2. Evaluate : sqrt(-16) + 3 sqrt(-25) + sqrt(-36) - sqrt(-625).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. 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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  18. 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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  19. 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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  20. If ((1+i)/(1-i))^3-((1-i)/(1+i))^3 =a+ib find a and b

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

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