Question

find sinh (log i) and log i log (1+i)
Q.12 only ignore Q11.​

Answer 1

Answer :

i ) → i

ii ) → (π/4)i•log2 - π²/8

Solution :

Please refer to the attachments .

Concept used :

• If Z = x + iy be a complex number then for the polar form x = r.cos∅ and y = r.sin∅ .

Thus ,

r² = x² + y²

ie. r = √(x² + y²)

And tan∅ = y/x

ie. ∅ = arctan(y/x)

Then in polar form , Z will be given as

Z = r(cos∅ + i.sin∅)

• Euler's formula :

e^(i∅) = cos∅ + i.sin∅

• De Moivre's theorem :

(cos∅ + i.sin∅)ⁿ = cos(n∅) + i.sin(n∅)

• sinhx = ½[e^x - e^(-x)]

• coshx = ½[e^x + e^(-x)]