Home
Class 11
MATHS
Find the principal argument of (1+isqrt(...

Find the principal argument of `(1+isqrt(3))^2dot`

Text Solution

Verified by Experts

Given that , `z= (1+isqrt(3))^(2)`
`rArr z= 1-3 +2isqrt(3) rArr z=-2+i2sqrt(3)`
`rArr tan alpha=|(2sqrt3)/(-2)|=|-sqrt(3)|=sqrt(3) " " [:' tan alpha = |(Im(z))/(Re(z))|]`
`rArr tan alpha = "tan"(pi)/(3) rArr alpha = (pi)/(3)`
`:' Re (z)lt0 "andIm(z)gt0`
`rArr arg(z)= pi-(pi)/(3) rArr = (2pi)/(3)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|16 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise LONG ANSWER TYPE QUESTIONS|14 Videos

  • BINOMIAL THEOREM

    NCERT EXEMPLAR|Exercise True/False|7 Videos

  • CONIC SECTIONS

    NCERT EXEMPLAR|Exercise Objective type|13 Videos

Similar Questions

Explore conceptually related problems

Find the principal argument of (1+i sqrt(3))^(2)

Find the principal argument of (-2i).

Principal argument of z=-1-i sqrt(3)

Find the principal value of: cot^(-1)(sqrt(3))

Find the principal value of tan^(-1)(-sqrt(3))

Find the principal value of : tan^(-1) sqrt(3)

Find the principal value of cot^(-1)(-sqrt3)

The principal argument of 2z^(2)+1-sqrt(3)i=0

If arg(z_(1))=170^(@) andarg (z_(2))=70^(@), then find the principal argument of z_(1)z_(2)