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Find the square root of the following co...

Find the square root of the following complex number: `\ 1+4sqrt(-3)`

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`sqrt(1+4(sqrt(-3)))=+-[sqrt(frac{abs(z)+Re(z)}{2})+isqrt(frac{abs(z)-Re(z)}{2})]`
`=+-[sqrt(frac{7+1}{2})+isqrt(frac{7-1}{2})]`
`=+-(sqrt(4)+isqrt(3))`
`=+-(2+sqrt(3)i)`
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. Find the square root of the following complex number: -5+12 i

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  2. Find the square roots of the following:8\ 6i

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  3. Find the square root of the following complex number: \ 1+4sqrt(-3)

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  4. Find the square root of the following complex number: -7-24 i

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  5. Find square root of 8-15 i

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  6. Find the square root of the following complex number: 1-i

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  7. Find the square root of the following complex number: -11-60sqrt(-1)

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  8. Find the square root of the following complex number: -i

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  9. Find the modulus and argument of each of the following complex number:...

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  10. Find the modulus and argument of each of the following complex number:...

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  11. Find the modulus and argument of each of the following complex number:...

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  12. Find the modulus and argument of each of the following complex number:...

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  13. Find the modulus and argument of the following complex number:(1+i)/(1...

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  14. Find the modulus and argument of the following complex number: 1/(1+i)

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

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

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  17. Write the following complex numbers in the polar form: \ 1+i

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

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  19. Find the modulus and principal argument of (1+i) and hence express it ...

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  20. Find the modulus and principal argument of -2i

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