University⏱ 4 min

Complex Exponential

e^z in the complex plane

○Not Started
Real part of exponent a: 0.30
Steps: 50
e(0.3+i)t=e0.3t(cos⁡t+isin⁡t)e^{(0.3+i)t} = e^{0.3t}(\cos t + i\sin t)
a>0: extspiraloutwarda > 0: \ ext{ spiral outward}

e^(a+bi)t = a spiral. If a=0: rotates on a circle. If a>0: spiral grows outward. If a<0: spiral winds inward.