# Ch 01: Number Systems

- 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)*