Home
Class 11
MATHS
Write the following complex numbers in t...

Write the following complex numbers in the polar form: `-1-i`

Text Solution

Verified by Experts

Modulus`abs(z)=sqrt((-1)^2+(-1)^2)=sqrt 2`
`tan alpha= abs(frac{Im(z)}{Re(z)})`
`tan alpha=1=>alpha=frac{pi}{4}`
The point representing `z` lies in the third quadrant.
Argument `theta` of `z` is `theta=-(pi-alpha)=-(pi-frac{pi}{4})=-(3pi)/{4}`
Polar form is `z=sqrt 2(cos(3pi)/4-i sin (3pi)/{4})`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COMBINATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|117 Videos

  • DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|236 Videos

Similar Questions

Explore conceptually related problems

Write the following complex numbers in the polar form: -3sqrt(2)+3sqrt(2)i

Express the following complex number in the polar form: (1+i)/(1-i)

Express the following complex number in the polar form: (i) (1+7i)/((2-i)^(2))( ii) (1+3i)/(1-2i)

Write down the following complex number in polar form: Quotient of 12(cos150^(@)+i sin150^(@)) and 3(cos60^(@)+i sin60^(@))

Express the following complex number in the polar form: (2+6sqrt(3i))/(5+sqrt(3)i)

Write down the following complex number in polar form: Product of 2(cos30^(@)+i sin30^(@)) and 3(cos90^(@)+i sin90^(@))

Convert each of the following complex numbers into polar form: {:((i),3,(ii),-5,(iii),i,(iv),-2i):}

Convert each of the following complex numbers in polar form: (i) -3 (ii) sqrt3+i (iii) i .

Put the following numbers in the polar form: -1-sqrt(3)i

Put the following numbers in the polar form: -1+i

Home
Profile