How do you simplify or combine pi/4 and tan^(-1) of 2?

Question

How do you simplify or combine pi/4 and tan^(-1) of 2?

I was thinking of changing pi/4 to tan^(-1) of 1. Then i got stuck.

Any ways of combining the two together to get a simplified answer?

Another question is that if modulus of (z-2+3i)=1 is there a loci to describe this thing since modulus of something should not give i where i=square root of -1?(related to complex numbers and argand diagram)

guess no one is smart enough to reply

oh great i understand now!

Answer 1

I think you mean

pi/4 + tan^1(2)

say x = pi/4+ a where a = tan^1(2)

taken tan of both sides

tan x = (tan pi/4 + tan a)/(1- tan pi/4. tan a)
= (1+2)/(1-1.2) = 3/(-1) or -3

x = tan ^-3 and x in 2nd quadrant

for the 2nd question there ia a locus and it is a circle
let z = x+iy
|z -2 + 3i| = | x+iy-2+3i|
(x-2)^2 + (y+3)^2 =1

so circle with centre (2,-3) and radius 1

Answer 2

Let's go to the second question because I have No answer for the first
z=x+yi so your expression is x-2+(3+y)i
whose modulus is(squared)
(x-2)^2 +(y+3)^2=1
This is a circunference with center(2,-3) and r=1