Tessa and Arnold

Justin's journey to find out what happened to Tessa was not only prompted by his love - it was also prompted by his suspicion that she was being unfaithful.  This suspicion is not very difficult for the audience to understand.  The very first scene in the movie depicts Tessa, in the company of another man, leaving Justin at an airport.  The conversation went like this:


Justin Quayle: Oh, thank you Arnold. I... I can manage that. But I still don't see why you couldn't wait a couple of weeks. Why go all the way up to Loki? 
Tessa Quayle: Well, we want to hear Grace Makanga speak, and she won't be coming to Nairobi.
Justin Quayle:  I see...
Tessa Quayle:  Oh sweetheart, don't bother to see us off.  It could be ages.
Justin Quayle:  Okay well... if you're sure.


After they share a hug and an exorbitant amount of kisses from Tessa, she walked towards the plane with Arnold.  It is clear from Justin's dialogue that he didn't think the trip had any purpose and he was hesitant about her departure.  When we watch Tessa and Arnold's interaction, we can guess why.  First, Arnold put his hand on Tessa's lower back and offered to carry her bag.  When Tessa hands it over, she placed her hand on Arnold's forearm while she said her last "goodbye"s to Justin.  These physical connections, in addition to Tessa's insistence that Justin not wait around to see the plane take off, make the whole scene questionable.


Another example of where Justin's insecurity comes from is during a scene at Justin and Tessa's house in Africa.  Justin had been working in his garden and walked past Tessa having a conversation with Arnold.  She says:

Tessa Quayle:  It's an outrageous thing.  It's like it's a marriage of convenience and all it produces are dead offspring.


Considering that the two had had a baby who died, Justin immediately assumed his wife was referring to their own marriage.  The fact that she was confiding in a man who she spent every day with did not help Arnold's cause.  One night, Justin waited up for Tessa until very late at night.  This is their conversation when Tessa finally returned:


(in the background, we hear Arnold say, "See you Tessa")
Justin Quayle: Hi
Tessa Quayle: Hi.  It's bloody awful weather.  You really shouldn't have waited up.  Good, then I think you should go to bed.  I'm safe home now, sweetheart.
Justin Quayle: No, you're drenched.  Look, take those wet things off.  Tessa, come to bed with me, please.
Tessa Quayle: I will, but there's, um, something I have to do first.  It's important.
Justin Quayle: Tessa, whatever it is that you and Arnold are doing, I'd like it to stop.


Considering that Justin does not know how Tessa is spending her days, that she was just dropped off late by a different man, and that she refused to go to bed with him, it can be understood that when he says "stop", Justin is asking Tessa to stop having an affair with Arnold.  Tessa, however, takes his comment to mean that he wants is working to rein her in and put a stop to her personal work.  The two end up in an argument and Tessa does not go to bed with Justin.


All of these scenes are proof that Justin believes Tessa and Arnold are having an affair when she is murdered.  This belief prompts him to begin to investigate her death.


Throughout his journey, Justin does find out that Arnold is gay, and therefore can not have been Tessa's lover.  Because this information comes after Justin is already in the midst of his investigation of his wife's death, it has no effect on his continuing questions about KDH.  The importance of Arnold and Tessa's relationship is that it helped to instigate Justin's curiosity about the murder and eventually lead to the unfolding of the pharmaceutical mystery.