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Convert z= (i-1)/(cos frac (pi)(3)+i sin...

Convert `z= (i-1)/(cos frac (pi)(3)+i sin frac (pi)(3))` in polar form.

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Value of sin frac (31 pi)(3) is :

Prove that sin frac (pi)(14) sin frac (3 pi)(14) sin frac (5pi)(14) sin frac (7pi)(14)=1/8 .

Prove that : sin frac (pi)(5) sin frac (2pi)(5) sin frac (3pi)(5) sin frac (4pi)(5) =5/16 .

The value of : (1+cos frac (pi)(6)) (1+cos frac (pi)(3))(1+cos frac (2pi)(3)) (1+cos frac (7pi)(6)) is:

The smallest positive integral value of ‘n’ such that [(1+sin frac (pi)(8)+i cos frac (pi)(8))/(1+sin frac (pi)(8)-i cos frac (pi)(8))]^n is purely imaginary is n =

Prove that : (1+cos frac (pi)(8)) (1+cos frac (3pi)(8)) (1+cos frac (5pi)(8)) (1+cos frac (7pi)(8))=1/8 .

Prove that : 3 sin frac (pi)(6) sec frac (pi)(3)-4 sin frac (5pi)(6) cot frac(pi)(4)=1 .

Prove that sin frac (pi)(10)+ sin frac (13 pi)(10)=-1/2 .

Prove that : 3 cos^2 frac (pi)(4)+ sec frac (2 pi)(3)+ 5 tan^2 frac (pi)(3) = 29/2 .

Prove that: 2cos frac (pi)(13)cos frac (9pi)(13)+cos frac (3pi)(13)+cos frac (5pi)(13)=0

MODERN PUBLICATION-COMPLEX NUMBERS-EXERCISE
  1. Solve the following equation : x^2-(3 sqrt2 -2i)x-6 sqrt2 i=0.

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  2. Solve the following equation : 2x^2-(3 +7i)x + (9i-3)=0.

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  3. Reduce (1/(1- 4i)-2/(1+i)) ((3-4i)/(5+i)) to the standard form .

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  4. Convert the following in the polar form : (1+7i)/(2-i)^2.

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  5. Convert the following in the polar form: (1+ 3i)/(1-2i)

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  6. If z1= 2 -i, z2= 1+ i, find |(z1+z2+1)/(z1-z2+1)|.

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  7. Let z1 = 2 -i, z2 = -2 + i. Find Im(1/(z1barz1))

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  8. If a + ib = ((x+i)^2)/(2x^2+1), prove that a^2+b^2 =((x^2+1)^2)/((2x^2...

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  9. Find the modulus of (1+i)/(1-i)-(1-i)/(1+i) .

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  10. Find the modulus and argument of (1+2i)/(1-3i).

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  11. Convert z= (i-1)/(cos frac (pi)(3)+i sin frac (pi)(3)) in polar form.

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  12. Find the non-zero integral solutions of |1-i|^x=2^x.

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  13. If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a^2 +...

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  14. If z1 =-3i, z2= 3 +4i and z3=2- 3i, verify that z1(z2+z3)=z1z2+z1z3.

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  15. If x-iy= sqrt((a-ib)/(c-id)) prove that (x^2+y^2)^2= (a^2+b^2)/(c^2+d^...

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  16. If a^2+b^2=1, prove that (1+b+ia)/(1+b-ia)= b + ia.

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  17. Solve the equation given below:- 3x^2 - 4x+20/3=0

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  18. Solve the equation given below:- x^2 -2x+3/2=0

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  19. Solve the equation given below:- 27x^2 -10x + 1 = 0

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  20. Solve the equation given below:- 21x^2-28x+10=0

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