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Exercise - 01

Practice Exercise

  1. if \(a\) and \(b\) are real numbers then \(a+b\) is a real no. This law is called

  2. If \(a\in R\) then multiplicative inverse of \(a\) is

  3. Which of the following is field?

  4. \(1>-1\implies -3>-5\), this property is called

  5. Let \(a\), \(b\), \(c\), \(d\) \(\in R\) then \(a=b\) and \(c=d\implies\)

  6. If \(Z_1=(x_1,y_1)\), \(Z_2=(x_2,y_2)\) where \(Z_1\cdotp Z_2\in C\) then \(Z_1+Z_2=\)?

  7. If \(Z_1=3-6i\) and \(Z_2=4+5i\) then \(Z_1Z_2=\)?

  8. If \(Z_1=(1,0)\), \(Z_2=(2,3)\) then \(Z_1Z_2=\)?

  9. \((3,5)+(0,4)=\)?

  10. Additive inverse of \((3,3)\) is \(C\) is

  11. If \(Z=(a,b)\) then multiplication inverse of \(Z\) is

  12. If \(Z=a+b\), then \(|Z|=\)?

  13. If \(Z=a+b\), then \(\overline{Z}=\)?

  14. \(i^{15}=\)?

  15. The value of \(i^{25}=\)?

  16. Conjugate of \((-3,4)\) is

  17. \((-i)^{31}\)

  18. The multiplicative inverse of \(1-3i\) is

  19. The value of \(i^{-29}\) is

  20. If \(Z\in C\) then \(Z\overline{Z}=\)?

  21. If \(Z_1,Z_2\in C\) then \(\overline{Z_1+Z_2}=\)?

  22. The value of \((3+2i)^3\) is

  23. \(C\) has no identity with respect to \(+\) other than

  24. The conjugate of $$ \frac{2+3i}{1-i} $$

  25. \((-1+\sqrt{-3})^4+\) \((-1-\sqrt{-3})^4=\)?

  26. The smallest positive \(k\) for which $$ \left(\frac{1+i}{1-i}\right)^k = 1 $$ is

  27. Set of even prime natural numbers is

  28. If \(n\) is any positive integer then the value of $$ \frac{i^{4n+1} - i^{4n-1} }{2}= $$ ?

  29. $$ \frac{\sqrt{18}}{\sqrt{72}} $$ is

  30. \(2\sqrt{-9}\times\sqrt{-16}=\)?

  31. $$ \left\vert\frac{1+i}{a+\frac{1}{i}}\right\vert= $$ ?

  32. $$ \left(\frac{1-i}{1+i}\right)^{100} =x+iy $$ then

  33. \(\{1,-1\}\) is closed with respect to

  34. \((\cos20+i\sin20)^5\) \(/(\cos30+i\sin30)^3=\)?

  35. The polar coordinates of point are \((2, 319)\) then the Cartesian coordinates of point are

  36. The set of rational numbers between two real numbers is

  37. Multiplicative inverse of non-zero elements \(a\in Z\) is

  38. The \(\{x\in R, x^2 +10=0\}\) is

  39. Additive identity on \(N\) is

  40. Additive inverse of \(2+\sqrt{3}\) is

  41. The multiplicative inverse of \(\sqrt{7}\) is

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