Home
Class 12
MATHS
Express sqrt2+ i =r cos theta +ir sin t...

Express `sqrt2+ i =r cos theta +ir sin theta`complex numbers in the polar form.

Text Solution

Verified by Experts

where r`sqrt(a^2+b^2)=sqrt((sqrt2)^2+1^2)=sqrt3`
`"and theta=tan^(-1)(b/a)=tan^(-1)(1/sqrt2)`
`:.sqrt2+i=sqrt3(costheta=isintheta),where tan` theta=1/sqrt2`
Promotional Banner

Topper's Solved these Questions

  • AREA UNDER PLANE CURVES (APPLICATION OF DEFINITE INTEGRALS)

    MBD PUBLICATION|Exercise QUESTION BANK|16 Videos
  • CONIC SECTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|179 Videos

Similar Questions

Explore conceptually related problems

Express isqrt3 =rcos theta +ir sin theta complex numbers in the polar form.

Express 1+isqrt2=r cos theta +sin theta complex numbers in the polar form.

Find dy/dx, x=a cos'theta', y=a sin theta.

intcosthetasqrt(5-sin^2theta)d theta

Show that the equation of the normal to x^(2/3) + y^(2/3) = a^(2/3) is y cos theta - x sin theta = a cos 2"theta" where theta is the inclination of the normal to x-axis.

Solve the following: cos 2theta - cos theta = sin theta - sin 2theta

Show that the equation of normal at any point on the curve x = 3 cos theta - cos^(3) theta, y = 3 sin theta - sin^(3) theta "is" 4 (y cos^(3) theta - x sin^(3) theta) = 3 sin 4 theta .

Evaluate : int (d theta)/(4cos^2 theta + 9 sin^2 theta)

Use Binomial theorem and De Moivre's theorem to show cos 3 theta=4 cos^3 theta-3cos theta , sin3theta=3sin theta-4 sin^3 theta Express cos ntheta as sum of product of power of sin theta "and" cos theta . Do the same thing for sin n theta.

MBD PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Express the 1-i points geometrically in the Argand plane.

    Text Solution

    |

  2. Show that the following number are equidistant from the origin :sqrt2 ...

    Text Solution

    |

  3. Express sqrt2+ i =r cos theta +ir sin thetacomplex numbers in the pol...

    Text Solution

    |

  4. Express 1+isqrt2=r cos theta +sin theta complex numbers in the polar ...

    Text Solution

    |

  5. Express isqrt3 =rcos theta +ir sin theta complex numbers in the polar...

    Text Solution

    |

  6. If 1,omega, omega^2 are the three cube roots of unity, prove that (1+o...

    Text Solution

    |

  7. (1-omega +omega^2)(1+omega-omega^2)=4

    Text Solution

    |

  8. (1-omega)(1-omega^2)(1-omega^4)(1-omega^5)=9

    Text Solution

    |

  9. (2+5omega +2 omega^2)^6=(2+2omega+5 omega^2)^6=729

    Text Solution

    |

  10. (1-omega+omega^2)(1-omega^2+omega^4)(1-omega^4+omega^2)….to 2n Factor...

    Text Solution

    |

  11. Prove that x^3+y^3+z^3-3xyz =(x+y+z)(x+omegay+omega^2z)(x+yomega^2+z ...

    Text Solution

    |

  12. If x=a+b, y=a omega+b omega^2,z=a omega^2+bomega show thatxyz =a^3+b^3

    Text Solution

    |

  13. If x=a+b, y=a omega+b omega^2,z=a omega^2+bomega show that x^2+y^2+z^2...

    Text Solution

    |

  14. If x=a+b, y=a omega+b omega^2,z=a omega^2+bomega show thatx^3+y^3+z^3=...

    Text Solution

    |

  15. If ax+by +cz=X,cx+by +az=Y,bx+ay+cz=Z show that (a^2+b^2+c^2-ab-bc-ca...

    Text Solution

    |

  16. If |z1|le1,|z2|le1"show that" |1-z1z2|^2-|z1-z2|^2=(1-|z1|^2)(1-|z2|^2...

    Text Solution

    |

  17. If a, b, c are complex numbers satisfying a+b+c=0 and a^2+b^2+c^2=0 th...

    Text Solution

    |

  18. What do the {z:|z-a|+|z+a|=2c} "where" |a|lt c represent?

    Text Solution

    |

  19. What do the{z:|z-a|-|z+a|=c} represent?

    Text Solution

    |

  20. What happen in (i)|a|ge c?

    Text Solution

    |