aspen

Difficult to say. Anxiety has driven me to do good things in the past. I get it whenever I am not totally scrupulous.
But it isn't a solid foundation. I have come to learn that my multiple scripture studies per day do me no good at all, because faith is not present when I'm acting out of fear.

Yes, anxiety is able to be complimentary with faith depending on the definition you use for anxiety (as has been pointed out by @Carborendum). I also like how Jacob later says the following (Jacob 4:18), "Behold, my beloved brethren, I will unfold this mystery unto you; if I do not, by any means, get shaken from my firmness in the Spirit, and stumble because of my over anxiety for you." (emphasis mine). Over anxiety is what I would consider heightened mental awareness where it entertains an increase in worry (the mind is no longer still).
Anxiety is a strength when it stems from a sincere earnest desire to build up the kingdom of God, or to serve our fellow brothers and sisters. As an individual that struggled with an over anxious personality I was grateful to know that my anxiety was not the issue, but when I allowed myself to become over anxious. It took me 4 years to overcome a level of over anxiety through the atonement. Little by little the Lord showed me how to strengthen this weakness.

I believe it all depends on how someone thinks of being anxious.   If by using anxious they mean to be willing and excited - then yes - I believe the two go together quite well.
But if someone thinks of anxiety to be more associated with fear - the two cannot go together any better than light and darkness.
 
The Traveler

We need to look at more than one definition of a word when interpreting the meaning.
Understanding these definitions may help answer the question.  The bolded phrases refer to one type of "anxious".  The underlined phrases refer to a different type of "anxious."
I believe the bolded is used in the phrase "anxiously engaged in a good cause." This is clearly something related to faith.
I believe the underlined is what Jacob was saying.  I don't know if I'd call it "complementary."  I'd say it is more disease vs cure.  Anxiety (fear) may be a disease (or ailment) of the soul.  Faith is the cure. I believe the article even says as much.
It says:
Don't be anxious.  (Don't worry about a thing). Pray instead with thanksgiving. So, certainly there is a relationship of some sort.  But "complementary"?  I'm not seeing it.

Interesting question!
I think the answer to that is where the anxiety comes from. If the anxiety is stemmed from feelings of wanting to fit in, look good, keep up with the Jones’ or other similar aspects than no. Any kind of debilitating anxiety that needs help from therapists or medicine to be controlled is not linked to faith.
But anxiety over the salvation of our fellow man or our need to repent is linked to faith, though should it get out of hand and we cannot function due to it, I would say we are straying into unhealthy territory.

When reading an article today the topic of faith and anxiety in some cases being complimentary attributes was covered. What do you think? We are told to be anxiously engaged in a good cause. What cases is anxiety a strength when paired with faith?
Jacob 1
5. For because of faith and great anxiety, it truly had been made manifest unto us concerning our people, what things should happen unto them.
6. And we also had many revelations, and the spirit of much prophecy; wherefore, we knew of Christ and his kingdom, which should come.
 
When reading an article today the topic of faith and anxiety in some cases being complimentary attributes was covered. What do you think?  What cases is anxiety a strength when paired with faith?
 
Here's the link to the article if any of you are interested. 
https://scripturenotes.com/overcoming-fud-through-the-proper-application-of-anxiety

When reading an article today the topic of faith and anxiety in some cases being complimentary attributes was covered. What do you think? We are told to be anxiously engaged in a good cause. What cases is anxiety a strength when paired with faith?
Jacob 1
5. For because of faith and great anxiety, it truly had been made manifest unto us concerning our people, what things should happen unto them.
6. And we also had many revelations, and the spirit of much prophecy; wherefore, we knew of Christ and his kingdom, which should come.
 
When reading an article today the topic of faith and anxiety in some cases being complimentary attributes was covered. What do you think?  What cases is anxiety a strength when paired with faith?
 
Here's the link to the article if any of you are interested. 
https://scripturenotes.com/overcoming-fud-through-the-proper-application-of-anxiety

I found this on an article I was reading this morning and thought it could add some insight. Here's a link to the article if you want to check it out.
 https://scripturenotes.com/how-do-i-meet-the-wants-and-needs-of-others
D&C 82:17 17. And you are to be equal, or in other words, you are to have equal claims on the properties, for the benefit of managing the concerns of your stewardships, every man according to his wants and his needs, inasmuch as his wants are just—
How do we determine if wants are just? In briefly analyzing this, I thought it would be helpful to visualize it this way.
 
 
 

Good point. I asked the site owner and he clarified this for me. When he wrote that he meant just hearing "theory" sounds a lot like holy speculation because we associate theory with speculation. But in this more in-depth article he explains in reality it's a harmonizing of gospel principles like music theory brings together all the principles. It's like the whole thing  comes together type of theory, not speculation. He's correcting the wording in the first article to not confuse people. He also said he would probably have done the graphic a little better to reflect this if he'd been thinking more clearly about it when he made the graphic.
https://scripturenotes.com/gospel-theory-a-harmony-of-principled-living

To add my 2 cents to this I found an awesome graphic on a site I do my scripture study on. Sometimes I learn more effectively with a visual so here goes. 
There are eternal laws and doctrines (teachings) rest upon those laws. Principles comes out of doctrines, and “a theory is founded on inferences drawn from principles which have been established on independent evidence” (Webster’s 1828 definition). A theory isn’t a man-made hypothesis like the theory of organic evolution or global warming, but it does feel a lot like holy speculation. What happens if I act on this true principle? What will the result be? A strengthening of faith?
To me, I think theory is the perfected understanding that comes from cause and effect relationships. If I do X, then Y happens. There are lots of "If" - "Then" statements in the scriptures I think correlate with this.
Here's a link to the site I got this from. It's worth checking out. https://scripturenotes.com/instructed-more-perfectly-in-theory-principle-doctrine-and-law