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Use trig ideutities to prove that e"ez2 01+ complex fuuction whose domain consists of all complex numbers Give An example except 0, aud Find all rools: (-9)4/2...

Question

Use trig ideutities to prove that e"ez2 01+ complex fuuction whose domain consists of all complex numbers Give An example except 0, aud Find all rools: (-9)4/2 Find the inverse function, f-'(2), of f(2) in thee complex plane? Prove your AnSWeE f(2) = e one-to-O1lC

Use trig ideutities to prove that e"ez2 01+ complex fuuction whose domain consists of all complex numbers Give An example except 0, aud Find all rools: (-9)4/2 Find the inverse function, f-'(2), of f(2) in thee complex plane? Prove your AnSWeE f(2) = e one-to-O1lC



Answers

Verify/prove that for the complex numbers $z_{1}=r_{1}(\cos \alpha+i \sin \alpha)$ and $z_{2}=r_{2}(\cos \beta+i \sin \beta)$ $\frac{z_{1}}{z_{2}}=\frac{r_{1}}{r_{2}}[\cos (\alpha-\beta)+i \sin (\alpha-\beta)]$

In this question. Unseeded The vision Zach equal toe a plus ivy and zero, but is equal a minus. I be does said then said, But is equal to a plus. I b in Glover a minus I e. No multiplying. It's really good, said Lord said. Part is equal. Go a script, Wyness Eyes God be square. No more games. The value a ice were ordered to minus one. It really gets doors that God is equal. Group is godless, be square does Moore said Zach, but is equally true on the route. A truly power for less into the bus. Oh no, again for said equal to a plus, I'd be sex. Sweat is equal to a bliss ivy whole Scared. We can write it. Service card is equal to its there. Less ice bad piece here. Less true. I e. B. No working the value. Oh, eyes very secret to minus one Big Exactly. Scott is equal to is where less Lou I a B minus feet square. Nos more do. This upset square is equal to a little eight to the power for less get to the powers for so defying that more dealers of second set but is equal to or get us or said square

Hello students in this question we have to show that the company imaginary part of the complex number is given by jet minus jet star. They were by this to iota. Okay so from the island regulation we can write that one by two iota of jack minus jet Start it is equal to one by two iota of jet which will be equal to a course tita plus iota a sine theta. Okay and minus of this judge star. So this will equals to eight course tita plus I owe to a scientist to and this is to Okay so from here after solving this will be cancelled out because cheetah so we will obtain that one by two iota of to iota a sine theta. Okay so hence from here we can represent that this is equal to a scientist to and it can be written as this function. Okay so hence we can see from the island equation, this is the answer for these questions. So if it were not complex number then this real number will not be obtained because we have determined this imaginary. But okay, so this is the answer for this problem. Okay, thank you.

Sentiment is Zidan deterred. Bar in on 100 of the part. And Clark do Can you get off? Sit whole power And we have to prove this using mathematical index and ah, let us first street for the And he called one alleged school toe for the convenience began. Lead zit vehicle tow A plus. I be now J D Power and that is city power M one, add This is it. Can you get off? It are just skips. Can you get our one on power? One does not change. Therefore, this is just can you get religious and arches are equal. Therefore a Sweeney's true Now let us true. SK is true If escape is true, it means congregate off the to the power k equals toe hold power K for this is a cold Let's market as relation one. Now we have to prove that this is true for any call to K plus one. And for Cape last one, Alexis will be j to the power K plus one conjugate and we have no proof. Are just so to be Jed conjugate on whole power K plus one. Now it can be detain AJ genital parquet into is it? Now we know that insert one into zero a zit to congregate equals so that one can do great into the to contribute flying this week it Zidlicky into said, And from relation one we have. Does it conjure grateful Power k into just kind of it? No. Your power is one poverty skates who we get zero conjugate our keep last one. So is there to congregate K plus one disease our required arges Therefore, when a scales true SK plus one is true, it means that sent its true hence given relation is proofed.

In discussion. Unsee that dietitian that equal toe a plus i b nos When did this upset is equal under is good for us Eat scared now again said but is equal to a minus I be formulas offset but is equal is good, Less violence e scare would be less of said What is it under a spare us? Be scared so defying? Thank more dealers upset is equal to it is a sag.


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