ECE 210: Complex Numbers & Phasors
Interactive Visualization for Signal Processing
Click or Drag to move the complex number
Z
Current State
Z = 1.00 + j1.00
Z = 1.41 e
j(0.25π)
Rectangular:
a = r
cos(
θ
),
b = r
sin(
θ
)
Exponential:
r = √
a
2
+ b
2
,
θ = tan
-1
(b/a)
Special Cases (Slide 5)
1 (e
j0
)
j (e
jπ/2
)
-1 (e
jπ
)
-j (e
j-π/2
)
1/√2 + j1/√2
-√3/2 + j1/2
Euler's Identity
e
jθ
= cos(θ) + j sin(θ)
≈ 1.41 [
0.707
+ j(
0.707
) ]