Complex number(exponential form)

[naspek]

Homework Statement

hey there.. I've try this question(below)..
but, i don't know whether my solution is correct or not..

Find a possible value for w that satisfies relation...
e^w = Z -->where z = 1 + 3^1/2


my solution...
r = 2
theta = pi/3
change z into exponential form...
z = 2e^i(pi/3)

hence, w = i(pi/3)

can anybody pleas guide me or verified my answer...

 

[rootX]

You mean
R.e^w = Z -->where z = 1 + 3^1/2.j

If r = 2
and w = j (pi/3)

Knowing
R . e^(j.t) = R. [cos(t) + j sin(t)],

2 . e^(j. pi /3) = ... ?

 

[naspek]

2 . e^(j. pi /3) = ... ?

2 . e^(j. pi /3) = 2[cos (pi/3) + i sin (pi/3)]

 

[rootX]

2 . e^(j. pi /3) = 2[cos (pi/3) + i sin (pi/3)]

Which equals z, hence verifying that your solution is good.

 

[naspek]

ok.. so.. is my answer is correct?

 

[Mentallic]

...verifying that your solution is good.

ok.. so.. is my answer is correct?

What rootX said is another way of saying "yes, it is correct"

 

[naspek]

thanks guys! really appreciate your help.. =)