Home
Class 11
MATHS
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.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    JBD PUBLICATION|Exercise EXAMPLE|36 Videos

  • BINOMIAL THEOREM

    JBD PUBLICATION|Exercise EXAMPLE|23 Videos

  • CONIC SECTIONS

    JBD PUBLICATION|Exercise EXAMPLE|35 Videos

Similar Questions

Explore conceptually related problems

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

JBD PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-EXAMPLE
  1. If z=x+iy and |z+a|=3|z-a|, show that 2(x^2+y^2)=5ax-2a^2.

    Text Solution

    |

  2. Solve 2x^2+x+1=0

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. If (x + iy)^3 = u + iv, then show that u/x +v/y = 4(x^2 - y^2)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Find the square root of i.

    Text Solution

    |

  9. Find the square root of 1+i.

    Text Solution

    |

  10. Find the squre root of 1+2sqrt(6)i.

    Text Solution

    |

  11. Convert each of the complex numbers given below in the polar form. Als...

    Text Solution

    |

  12. Convert each of the complex numbers given below in the polar form. Als...

    Text Solution

    |

  13. Convert each of the complex number -16/(1+isqrt3) into polar form. Als...

    Text Solution

    |

  14. If ((1+i)/(1-i))^3-((1-i)/(1+i))^3=x+iy, then find (x,y)

    Text Solution

    |

  15. If (x+iy)^(1/3)=a+ib, where a,b,x, y in R, show that x/a-y/b=-2(a^2+b^...

    Text Solution

    |

  16. If z=x+iy and |z|=1, show that the complex number z1=(z-1)/(z+1) is pu...

    Text Solution

    |

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

    Text Solution

    |

  18. If the imaginary part of (2z+1)/(iz+1) is -2, then the locus of the po...

    Text Solution

    |

  19. If the complex number z1 and z2be such that arg(z1)-arg(z2)=0, then sh...

    Text Solution

    |

  20. Solve the system of equations Re(z^2)=0, |z|=2.

    Text Solution

    |