Question

Z=5-5i and w=radical3-i find z/w and product of zw

Answer 1

`z=5-5i=5(1-i)=5\sqrt2e^(-i\pi/4)`

`w=\sqrt3-i=2\left(\frac{\sqrt3}2-\frac12i\right)=2e^(-i\pi/6)`


`\implies\frac zw=(5\sqrt2e^(-i\pi/4))/(2e^(-i\pi/6))=\frac5{\sqrt2}e^(-i\pi/12)`

`\implies\frac zw=\frac{5+5\sqrt3}4-\frac{5\sqrt3-5}4i`


`\implies zw=10\sqrt2e^(-i5\pi/12)=5\sqrt3-5-(5+5\sqrt3)i`