Question

QUESTION 7. [7] Find all solutions to the equation cosh z = i. Express your answer(s) in rectangular (cartesian) form and make a neat sketch showing where the solutions lie in the complex plane. It is acceptable, but not necessary, to consider this exercise as finding and plotting all values of cosh-li.

Answer 1

cosha la = i = cash catiy) = coshacosy risinha siny = i (2-45 of above is obtained by of hyperbolic equation, formule ded" functions) - coshacosy = 0 & sinha siny - cosha to & XEIR 1 KEZ - cosyo - Y= (2+1) 7 Put this in sinha siny=1 - sinha sin ((+1) 7) = 1 - (sinha) (-1) * = 1 when sinha = (1 - a= sinh" (1) when k every & na sinh-1(-1) when k odd. (: siht sinun is 1-1 Function) =) a= 0.88 when I ever. f n= – 0.88 when k odd >>2= 0.88 + (48+1) 130 2= -8.88 + (45+3) are solutias 1562 ] of cost cosha= i

- INT No MSG- o the sults Pons f bones represents of cashazi . They lies on the line f sinki-1(1) with odd point with y-anis x= sinh (-1) intersectia