====== Ch 01: Number Systems ======
<list-group>
  * Simplify $(i)^{19}$   --- //BISE Gujrawala(2015)//
  * If $z$ be a complex number then prove that $\overline{z_1 + z_2}=\overline z_1 +\overline z_2$   --- // BISE Sargodha(2015)//
  * Simplify $\frac{2}{\sqrt{5}+\sqrt{-8}}$ in the form of $a+ib$    --- // BISE Sargodha(2015)//
  * Simplify by justify each step $\frac{\frac{1}{a}-\frac{1}{b}}{1-\frac{1}{a}\frac{1}{b}}$   ---   // BISE Sargodha(2015)//
  * Find multiplicative inverse $(\sqrt{2}, -\sqrt{5})$  ---  //BISE Sargodha(2015)//
  * Does the set $\{0,-1\}$ possess the closure property with respect to "+" and "-".  --- // BISE Lahore(2017)//
  * Find multiplicative inverse of $a \div ib$  ---  // BISE Lahore(2017)//
  * Simplify $(-1)^\frac{-21}{2}$  ---  // BISE Sargodha(2016)//
  * Find multiplicative inverse of $(0,1)$  ---    // BISE Sargodha(2016)//
  * Does the set $\{1,-1\}$ possess the closure property with respect to "+" and "-".  --- // BISE Sargodha(2016)//
  * Prove that $|z_1z_2|=|z_1||z_2|$  ---   // BISE Lahore(2017)//

  * Express $1+i\sqrt{3}$ in the polar form   ---   // FBISE (2016)//

  * Simplify by using De Moivre's Theorem $(-\frac{1}{2}+\frac{\sqrt{3}}{2}i)^3$  ---  // FBISE (2017)//
</list-group>
{{tag>FSc FSc_Part1 Important_Questions_FSc_1}}