Question

how to factorise m^4+4?

Answer 1

One way to look at it is like this:

m4+4=0⟹m4=−4⟹m2=±2i.

But

m2=2i⟹m=±2–√i√.

Also,

m2=−2i⟹m=±i2–√i√.

Now you can use that fact that there are two square roots of i,

1+i2–√ and 1+i−2–√

to simplify each possibility, and get the 4 values of m you mentioned