convert the complex number Z= -1-iroot3 into polar form and represent them in argand diagram - Maths - Complex Numbers and Quadratic Equations

Question

convert the complex number Z= -1-iroot3 into polar form and
represent them in argand diagram

Manosh T M · Accepted Answer

Dear student

We have z=a+ib in general for a complex number Here z=-1-i3Then a=-1 and b=-3Now in polar form z=reiθand reiθ=r(cosθ+isinθ)Then here r(cosθ)=-1 and r(sinθ)=-3Now we have r2=r(cosθ)2+r(sinθ)2r2=-12+-32r2=1+3=4r=4=2Now we have r=2Againr(cosθ)=-1⇒2cosθ=-1⇒cosθ=-12Then θ=cos-1-12⇒θ=2π3=120°Thus the polar form is z=reiθ=2ei2π3
The argand plane is as
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_588b1bb97882e%20png"
style="width: 300px; height: 237px;">

Regards