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Find the real value of a for which 3i^3-...

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

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RD SHARMA ENGLISH-COMPLEX NUMBERS-All Questions
  1. For any two complex numbers z1\ a n d\ z2 and any two real numbers a ,...

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  2. If n in NN ,then find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3).

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

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  4. If |z|=2 and arg (z)=pi/4 , find z.

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  5. Write the argument of (1+isqrt(3))(1+i)(costheta+isintheta).

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  6. The value of (1+i)(1+i^2)(1+i^3)(1+i^4) is a. 2 b. 0 c. 1 d. i

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  7. If (3+2i sintheta)/(1-2i sintheta) is a real number and 0lt theta lt 2...

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  8. If sqrt(a+i b)=x+i y ,\ then possible value of sqrt(a-i b) is a. x^2+...

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  9. If z=cos(pi/4)+isin(pi/6) , then a. |z|=1, arg(z)=\ pi/4 b. |z|=1, arg...

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  10. The polar form of (i^(25))^3 is a. cos(pi/2)+isin(pi/2) b. cospi+i\ si...

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  11. If i^2=-1, then the sum i+i^2+i^3+... upto 1000 terms is equal to a. 1...

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  12. If z=(-2)/(1+isqrt(3)) , then the value of "arg"(z) is a. pi b. pi/4 c...

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  13. If a=costheta+isintheta, then (1+a)/(1-a) is: (a). cot(theta/2) (b). ...

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  14. If (1+i)(1+2i)(1+3i)...(1+n i)=a+i b , then the value of; 2. 5. 10. 17...

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  15. If ((a^2+1)^2)/(2a-i)=x+i y , then x^2+y^2 is equal to a. ((a^2+1)^4)/...

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  16. The principal value of the amplitude of (1+i) is A. pi B. pi/(12) C...

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  17. The least positive integer n such that ((2i)/(1+i))^n is a positive in...

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  18. If z is a non zero complex, number then |(|barz |^2)/(z barz )| is eq...

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  19. If a=1+i , then a^2 equals A. 1-i B. 2i C. (1+i)(1-i) D. (i-1)

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  20. If (x+i y)^(1//3)=a+i b ,\ then\ x/a+y/b is a. 0 b. 1 c. -1 d. none o...

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