第1题Writethenumberinpolarformwithargumentbetween0and2π.-3+3i第2题Findpolarformsforzw,z/w,and1/zbyfirstputtingzandwintopolarform.z=4√（3)-4iw=8i

Question

第1题
Write the number in polar form with argument between 0 and 2π.
-3 + 3i
第2题
Find polar forms for zw,z/w,and 1/z by first putting z and w into polar form.
z =4√（3) - 4i w = 8i

Answer 1

Write the number in polar form with argument between 0 and 2π.
把这个数写成极径、极角形势（即复数的指数形式）极角要在0 和 2π 之间
-3 + 3i =3√2 e^(3πi/4)
Find polar forms for zw,z/w,and 1/z by first putting z and w into polar form
先把z和w表示成指数形式,而后找到下列数的指数形式：zw,z/w,1/z.
z=4√3 - 4i = 8 (√3/2 - i /2) = 8 e^(11πi/6)
w = 8i = 8e^(πi/2)
所以 zw = 8 e^(11πi/6) 8e^(πi/2) = 64 e^[ i (11π/6 + π/2) ] = 64 e^(πi/3)
z/w = 8 e^(11πi/6) / [ 8e^(πi/2) ] = e^[i (11π/6 - π/2) ] = e^(4πi/3)
1/z = 1/[ 8 e^(11πi/6) ] = (1/8) e^(-11πi/6) = (1/8) e^(πi/6)