COMPLEX NUMBER, Sn dey solution

 Mathematics (SOURENDRANATH NATH DE) is a very famous book of  West Bengal board  and Students also like this book. So we are here to provide you some help in the solution of sn dey.

HOME (click here)

FOR 4 MARKS (click here)

FOR 5 MARKS (click here)


1. Do you think 4 as a complex number? If so why?

2.i  If x, y are real and x+iy=-i(-2+3i), find x and y.

2.ii If x,y are real and x+iy=(5/(-3+4i)), find x and y.

3. If (1+i)(2+i)(3+i)….(n+i)=a+ib , show that , 2 . 5 . 10….(n^2+1)=a^2+n^2

4. Prove that, `|frac{x-iy}{-x+iy}|=1`

5. if Z=`frac{2+i}{-2+i}` , find conjugate Z in the form a+ib

6. Express in the form A+iB (A, B are real):
6.i `left(1-iright)^3`

6.ii `frac1{1+i}+frac{1+i}i`

6.iii `frac{x+iy}{y-ix}“left(x^2+y^2ne0right)`

6.iv `frac i{2+i}+frac3{1+4i}`

6.v `frac{sqrt3-isqrt2}{2sqrt3-isqrt2}` `frac1{1-costheta-isintheta}`

7. Find the conjugate:
i. `sqrt{-5}-2`

ii. `2-isqrt3-sqrt2`


8. Simplify:
i. `frac{i+i^2+1^3+1^4}{1+i}`



iv. `left(1+iright)^{-2}-left(1-1right)^{-2}`


9. If x, y are real and (x+3i) and (-2+iy) are conjugate of each other , find x and  y.

10. Find the least positive integral value of n so that `left(frac{1+i}{1-i}right)^n=1`

11. Find the modulus:
i. `2sqrt2-isqrt6`




12. Find the arguments of each of the following complex number:
i. 2-2i

ii. -3-3i

iii. (1+i)`left(sqrt3+iright)`

iv. `frac{sqrt3+i}{-1-isqrt3}`

13. If a=`frac{1+i}{sqrt2}` , show that `a^6+a^4+a^2+1=0`

14. Find the cube root of -1 and 27

15. Factorise `a^2+1`

16. If 1,w,`w^2` denote the cube root of unity, find the roots of `left(x+5right)^3+27=0`

Leave a Reply

You cannot copy content of this page