Question

1) Find the square root of the following complex numbers 3+2√10 i​

Answer 1

Answer:

I hope this may helps you, also don't forget to mark my answer as Brainlist :)

Step-by-step explanation:

Your "and so on" could go like this:

{x2−y2=3,2xy=210−−√.

Then squaring and adding both,

x4−2x2y2+y4+4x2y2=(x2+y2)2=49,

so that

x2+y2=±7.

Solving with the help of the first,

x2=5,y2=2 or x2=−2,y=−5.

This leaves the possibilities

x=±5–√,y=±2–√.

By the second equation, we know the signs are synchronized, hence

5–√+i2–√ or −5–√−i2–√.

More generally,

{x2−y2=u,2xy=v.

yields

u2=12(v2+u2−−−−−−√+u),v2=12(v2+u2−−−−−−√−u),

and

x=±12(v2+u2−−−−−−√+u)−−−−−−−−−−−−−−√,y=±12(v2+u2−−−−−−√−u)−−−−−−−−−−−−−−√,

where the sign of xy must match the sign of v.