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COMPLEX MATH and REAL ANALYSIS



(a) Find all the values of z ∈ C

for which sin(z)=cosh(4)


(b) Find all the values of z ∈ C for which cos z is (i) real values and (ii) purely imaginary.


(c) Let S=(x,y)R2xR QandyZ Giving full reasons for your assertions, prove that S is uncountable.

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SOLUTION .
( a) To find all values of ZEC for which
Sin (z ) = Cosh ly)
Soin.
Let z = 2 +14
Sin (z) = Sin(xtiy)
= finn Cosiy + Cos n siniy
= Sink Coshy + i Cosx Sindy
= Cosh (4 ) [given]
" ....

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