# 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)
• fsc-part1-ptb/important-questions/ch01-number-systems