Question #0f1ea Precalculus Complex Numbers in Trigonometric Form Complex Number Plane 1 Answer Cesareo R. Dec 29, 2016 See below. Explanation: Calling #z=x+iy# we have #abs(z)=sqrt(z bar(z)) = sqrt((x+iy)(x-iy))=sqrt(x^2+y^2)# so #abs(z)=1# corresponds to a circle centered at the origin of coordinates, with radius 1. Squaring both sides #x^2+y^2= 1# Answer link Related questions What is the complex number plane? Which vectors define the complex number plane? What is the modulus of a complex number? How do I graph the complex number #3+4i# in the complex plane? How do I graph the complex number #2-3i# in the complex plane? How do I graph the complex number #-4+2i# in the complex plane? How do I graph the number 3 in the complex number plane? How do I graph the number #4i# in the complex number plane? How do I use graphing in the complex plane to add #2+4i# and #5+3i#? How do I use graphing in the complex plane to subtract #3+4i# from #-2+2i#? See all questions in Complex Number Plane Impact of this question 1222 views around the world You can reuse this answer Creative Commons License