var("t")

def myviewer( r, j, c1, c2 ):
    z1 = r + j*sqrt(-1)
    z2 = r - j*sqrt(-1)

    f(t) = c1*exp( z1*t ) + c2*exp( z2*t )
    g(t) = c1*exp( real_part(z1)*t ) + c2*exp( real_part(z2)*t ) 

    P1 = plot( real_part( f(t) ), 0, 10, ymin=-6, ymax=6, gridlines="minor")
    P2 = plot( g(t), 0, 10, ymin=-6, ymax=6, gridlines="minor", linestyle="--")
    P3 = plot( -g(t), 0, 10, ymin=-6, ymax=6, gridlines="minor", linestyle="--")

    P=P1 + P2 + P3
    show(P)
    
myviewer( -0.25, 4, 5, 6 )