How do you change #10z^4# into polar coordinates where #z = 2 +4i#? Precalculus Complex Numbers in Trigonometric Form Trigonometric Form of Complex Numbers 1 Answer VinÃcius Ferraz May 23, 2017 #4000(cos theta + i sin theta)# Explanation: Let's square it two times. #z^2 = 4 + 16i - 16# #z^4 = (-12 + 16i)^2 = 144 - 24*16i - 256 = -112 - 384i# #10z^4 = -1120 - 3840i = w# #|w| = sqrt{1120^2 + 3840^2} = 4000# #tan (text{arg } w) = 3840/1120 = 24/7# #theta = text{arg } w = pi + arctan frac{24}{7}# Answer link Related questions How do I find the trigonometric form of the complex number #-1-isqrt3#? How do I find the trigonometric form of the complex number #3i#? How do I find the trigonometric form of the complex number #3-3sqrt3 i#? How do I find the trigonometric form of the complex number #sqrt3 -i#? How do I find the trigonometric form of the complex number #3-4i#? How do I convert the polar coordinates #3(cos 210^circ +i\ sin 210^circ)# into rectangular form? What is the modulus of the complex number #z=3+3i#? What is DeMoivre's theorem? How do you find a trigonometric form of a complex number? Why do you need to find the trigonometric form of a complex number? See all questions in Trigonometric Form of Complex Numbers Impact of this question 1427 views around the world You can reuse this answer Creative Commons License