Question

If z=re^i theta then the value of modulus of e^iz

Answer 1

Answer:

e^(-rsin1)

Step-by-step explanation:

Hi,

Given z = re^i

e^iz = e^(i*re^i)  

But, e^iФ = cosФ + i sinФ, so

e^iz = e^ir(cos1 + isin1)

=e^(ircos1 - rsin1)

e^(-rsin1). e^(ircos1)

Modulus of e^iz will be = |e^(-rsin1). e^(ircos1)|

= e^(-rsin1) , since |e^(ircos1)| = 1.

Hope, it helps !