Home
Class 12
MATHS
For z(1)=""^(6)sqrt((1-i)//(1+isqrt(3)))...

For `z_(1)=""^(6)sqrt((1-i)//(1+isqrt(3))),z_(2)=""^(6)sqrt((1-i)//(sqrt(3)+i))`, `z_(3)= ""^(6)sqrt((1+i) //(sqrt(3)-i))`, prove that `|z_(1)|=|z_(2)|=|z_(3)|`

Text Solution

Verified by Experts

`|z_(1)| = |(1-i)/(1+isqrt(3))|^((1)/(6)) = |(sqrt(2))/(2)| = 2^(-(1)/(12))`
Similary,
`|z_(2)| = 2^((1)/(12)), |z_(3)| = 2^(-(1)/(12))`
Hence, the result.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.7|6 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.8|11 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.5|12 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

Similar Questions

Explore conceptually related problems

For Z_(1)=6sqrt((1-i)/(1+i sqrt(3)));Z_(2)=6sqrt((1-i)/(sqrt(3)+i));Z_(3)=6sqrt((1+i)/(sqrt(3)-i)) which of the following holds good?

Let z_1=((1+sqrt(3)i)^2(sqrt(3)-i))/(1-i) and z_2=((sqrt(3)+i)^2(1-sqrt(3)i))/(1+i) then

The complex number, z=((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(3)i))

If z_(1)=iz_(2) and z_(1)-z_(3)=i(z_(3)-z_(2)), then prove that |z_(3)|=sqrt(2)|z_(1)|

If |z-3i|

If z = ((1)/(sqrt(3)) + (1)/(2)i)^(7) + ((1)/(sqrt(3))-(1)/(2)i)^(7) , then

If z_(1)=sqrt(2)((cos pi)/(4)+i sin((pi)/(4))) and z_(2)=sqrt(3)((cos pi)/(3)+i sin((pi)/(3))) then |z_(1)z_(2)|=

If z(2-2sqrt(3i))^(2)=i(sqrt(3)+i)^(4), then arg(z)=

If z=pi/4(1+i)^4((1-sqrt(pi)i)/(sqrt(pi)+i)+(sqrt(pi)-i)/(1+sqrt(pi)i)),then"((|z|)/(a m p(z))) equal