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Find the modulus and the arguments of t...

Find the modulus and the arguments of the complex number `z=-sqrt(3)+i`

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Here, `z = -sqrt(3) + i`
Comparing it with polar form, we get,
`rcostheta = -sqrt3 and rsintheta = 1`
Squaring and adding these two terms, we get,
`r^2cos^2theta+r^2sin^2theta = 4 `
`r^2(cos^2theta+sin^2theta) = 4`
`r^2 = 4=> r = 2`
So, modulus is `2`.
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NCERT ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Convert of the complex number in the polar form: -1-i

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  2. Find the modulus and the arguments of the complex number z = - 1 - is...

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  3. Find the modulus and the arguments of the complex number z=-sqrt(3)+i

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  4. Convert the complex number z=(i-1)/(cospi/3+isinpi/3)in the polar form...

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  5. Find real theta such that (3+2isintheta)/(1-2isintheta)is purely real...

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  6. If x + i y =(a+i b)/(a-i b),prove that x^2+y^2=1.

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  7. Find the modulus and argument of the complex numbers : (i) (1+i)/(1-i...

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  8. Find the conjugate of ((3-2i)(2+3i))/((1+2i)(2-i)).

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  9. Solve: sqrt(5)x^(2) + x + sqrt(5) = 0

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

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  11. Convert of the complex number in the polar form: -1 + i

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  12. Express of the complex number in the form a + i b. (-2-1/3i)^3

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  13. Find the multiplicative inverse of the complex number. 4 - 3i

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  14. Find the multiplicative inverse of the complex number. sqrt(5)+3i

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  15. Find the multiplicative inverse of the complex number. i

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  16. Express the following expression in the form of a + i b((3+isqrt(5))(3...

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

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  18. Solve the equation:x^2+x+1/(sqrt(2))= 0

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  19. Solve the equation:sqrt(3)x^2-sqrt(2)x+3sqrt(3)= 0

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  20. Convert of the complex number in the polar form: - 3

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