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.
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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}`
6.vi `frac1{1-costheta-isintheta}`
7. Find the conjugate:
i. `sqrt{-5}-2`
ii. `2-isqrt3-sqrt2`
iii.`frac{2-i}{left(1-2iright)^2}`
8. Simplify:
i. `frac{i+i^2+1^3+1^4}{1+i}`
ii.`left(1+i^3right)left(1+frac1iright)^2left(i^4+frac1{i^4}right)`
iii.`left(1+iright)^2+left(frac{1-i}{1+1}right)^2`
iv. `left(1+iright)^{-2}-left(1-1right)^{-2}`
v.`left(frac{1+i}{1-i}right)^2+left(frac{1-i}{1+1}right)^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`
ii.`left(sqrt5+isqrt3right)left(-2+iright)`
iii.`frac{1-i}{3-4i}`
iv.`frac2{1+costheta+isintheta}`
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`
