若复数z满足3z^6+2iz^5-2z-3i=0,则|z|=________.

问题描述:

若复数z满足3z^6+2iz^5-2z-3i=0,则|z|=________.

方程可以化为:z^5(3z+2i) = 2z+3i
z^5 = (2z+3i)/(3z+2i)
|z|^10 = |2z+3i|²/|3z+2i|²
设z=x+yi
则 上述等式右边 = [4x²+(2y+3)²] / [9x²+(3y+2)²]
分子 - 分母 = -5(x²+y²) + 5 = 5(1-|z|²)
当 |z|>1时,分子-分母