Question

I got this answer for a problem, and I'm not sure if it's right.
Can someone tell me if I'm correct?
1.(2+4i / 3-i)
= 6/7+5/7i

Answer 1

2+41 /(3-i)
rationalize
(2+4i)(3+i)/10= (6+2i+12i-4)/10=
=(2+14i)/10

Answer 2

Ahh!
I'm confused about this math stuff:/
it's my first time trying these algebra problems.
I'm trying to go by the teacher's examples.
Can You tell me if these are right:p?
2. (7-√-15)^2
= 34+14i√15i

3.4+√-20 / 2
=2+2.5√4i

Answer 3

another way, in polar form:

(2+4i)=sqrt20@arctan2
(3-i)=sqrt10@arctan(-1/3)

so (2+4i)/(3-i)=sqrt20/sqrt10 @ (arctan2-arctan-1/3)=sqrt2 @(1.11rad-(-.321))
= sqrt2 @1.43rad=sqrt2 @ 81.9 deg

Now converting this (only to compare with the above)
= sqrt2 (cos81.9+isin81.9)
= (.198+i*1.40)
and the above is .2+i1.40

I rounded the angles on the arctan conversions...

Answer 4

2. (7-√-15)^2
= 34+14i√15i ????

(7-isqrt15)^2=49-15-2isqrt15=34-2i sqrt15

3.4+√-20 / 2
=2+2.5√4i ????

4/2+1/2 i sqrt20=2+.5i*sqrt4*sqrt5
= 2+i sqrt5

Answer 5

(7-isqrt15)^2=49-15-2isqrt15??
I get 49-15- 14√15 i