kev-kun
Member
Hi all, bit confused on how to answer because my teacher rushes a LOT! Any help would be great!
<img src="http://latex.codecogs.com/gif.latex?$1)\&space;Find\&space;the\&space;fourth\&space;root\&space;of\&space;1+i\sqrt3&space;\\$" title="$1)\ Find\ the\ fourth\ root\ of\ 1+i \sqrt3 \\$" />
<img src="http://latex.codecogs.com/png.latex?\\2)\(a)If\&space;w\&space;is\&space;a\&space;complex\&space;root\&space;of\&space;1.\&space;Find\&space;w\&space;in&space;\&space;polar&space;\&space;form&space;\&space;and\&space;show\&space;that\\&space;\indent(i)\&space;i+w+w^2=0\\&space;\indent(ii)\&space;(w^2)^2=0&space;\\&space;(b)Using\&space;these\&space;properties\&space;of&space;\&space;w,\&space;show\&space;that\\&space;\indent(i)(1-w)(1-w^2)(1-w^4)(1-w^5)=9&space;\\&space;\indent&space;(ii)\&space;(1+2w+3w^2)(1+2w^2+3w)=3&space;\\&space;\indent&space;\(iii)\&space;(1+w)(1+2w)(1+3w)(1+5w)=21" title="\\2)\(a)If\ w\ is\ a\ complex\ root\ of\ 1.\ Find\ w\ in \ polar \ form \ and\ show\ that\\ \indent(i)\ i+w+w^2=0\\ \indent(ii)\ (w^2)^2=0 \\ (b)Using\ these\ properties\ of \ w,\ show\ that\\ \indent(i)(1-w)(1-w^2)(1-w^4)(1-w^5)=9 \\ \indent (ii)\ (1+2w+3w^2)(1+2w^2+3w)=3 \\ \indent \(iii)\ (1+w)(1+2w)(1+3w)(1+5w)=21" />
<img src="http://latex.codecogs.com/gif.latex?$1)\&space;Find\&space;the\&space;fourth\&space;root\&space;of\&space;1+i\sqrt3&space;\\$" title="$1)\ Find\ the\ fourth\ root\ of\ 1+i \sqrt3 \\$" />
<img src="http://latex.codecogs.com/png.latex?\\2)\(a)If\&space;w\&space;is\&space;a\&space;complex\&space;root\&space;of\&space;1.\&space;Find\&space;w\&space;in&space;\&space;polar&space;\&space;form&space;\&space;and\&space;show\&space;that\\&space;\indent(i)\&space;i+w+w^2=0\\&space;\indent(ii)\&space;(w^2)^2=0&space;\\&space;(b)Using\&space;these\&space;properties\&space;of&space;\&space;w,\&space;show\&space;that\\&space;\indent(i)(1-w)(1-w^2)(1-w^4)(1-w^5)=9&space;\\&space;\indent&space;(ii)\&space;(1+2w+3w^2)(1+2w^2+3w)=3&space;\\&space;\indent&space;\(iii)\&space;(1+w)(1+2w)(1+3w)(1+5w)=21" title="\\2)\(a)If\ w\ is\ a\ complex\ root\ of\ 1.\ Find\ w\ in \ polar \ form \ and\ show\ that\\ \indent(i)\ i+w+w^2=0\\ \indent(ii)\ (w^2)^2=0 \\ (b)Using\ these\ properties\ of \ w,\ show\ that\\ \indent(i)(1-w)(1-w^2)(1-w^4)(1-w^5)=9 \\ \indent (ii)\ (1+2w+3w^2)(1+2w^2+3w)=3 \\ \indent \(iii)\ (1+w)(1+2w)(1+3w)(1+5w)=21" />
