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Express the following in the standard fo...

Express the following in the standard form `a+i b :1/(-2+sqrt(-3))`

Text Solution

Verified by Experts

Given that,
`1/(-2+sqrt(-3))`
`=1/[-2+ sqrt(-1) sqrt(3)]`
`=1/[-2+isqrt3]` [since, `sqrt(-1)=i`]
...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. Express the following in the standard form a+i b :((3-2i)(2+3i))/((1+2...

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  2. Express the following in the standard form a+i b :(5+4i)/(4+5i)

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  3. Express the following in the standard form a+i b :1/(-2+sqrt(-3))

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  4. Express the following in the standard form a+i b :((3+isqrt(5))(3-isqr...

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  5. Express the following in the standard form a+i b :((1+i)^2)/(3-i)

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  6. Express the following in the standard form a+i b :(1/(1-2i)+3/(1+i))((...

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  7. Express the following in the standard form a+i b :1/(1-costheta+2i sin...

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  8. Express (1-2i)^(-3) in the standard form a+i bdot

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  9. Perform the indicated operation and find the result in the form a+i b ...

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  10. Perform the indicated operation and find the result in the form a+i b ...

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  11. Multiply 3-2i by its conjugate.

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  12. Find the real numbers x\ a n d\ y , if (x-i y)(3+5i) is the conjugate ...

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  13. Find the multiplicative inverse of the complex number: 3+2i

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  14. Find the multiplicative inverse of the following complex number: (2+sq...

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

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  16. If x+i y=sqrt((a+i b)/(c+i d)) prove that (x^2+y^2)^2=(a^2+b^2)/(c^2+d...

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  17. Find the least positive value of n if ((1+i)/(1-i))^n=1.

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  18. Find real theta such that (3+2i\ sintheta)/(1-2i\ sintheta) is purely ...

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  19. If (1+i)(1+2i)(1+3i)(1+n i)=(x+i y) , Show that 2.5.10 ..... (1+n^2)=x...

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  20. Find the value of x^3+7x^2-x+1,\ w h e n\ x=1+2idot

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