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

2+41 /(3-i)

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

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

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...

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

(7-isqrt15)^2=49-15-2isqrt15??

I get 49-15- 14√15 i

To determine if your answer is correct, we can simplify the expression (2 + 4i) / (3 - i) and compare it to the result you provided, which is 6/7 + 5/7i.

To simplify the expression, we can utilize complex number conjugates. The complex conjugate of a number a + bi is a - bi.

So, the complex conjugate of 3 - i is 3 + i.

To simplify the expression, multiply both the numerator and denominator by the complex conjugate of the denominator, which gives us:

((2 + 4i) / (3 - i)) * ((3 + i) / (3 + i))

Expanding this, we get:

((2 + 4i) * (3 + i)) / ((3 - i) * (3 + i))

Now we can multiply each expression:

The numerator becomes (2 * 3) + (2 * i) + (4i * 3) + (4i * i) = 6 + 2i + 12i + 4i^2
Simplifying the numerator further: 6 + 2i + 12i + 4i^2 = 6 + 14i + 4i^2

The denominator becomes (3 * 3) + (3 * i) - (i * 3) - (i * i) = 9 + 3i - 3i - i^2
Simplifying the denominator further: 9 + 3i - 3i - i^2 = 9 - i^2

We know that i^2 is equal to -1, so substituting this back in, we have:

6 + 14i + 4i^2 / 9 - i^2
= 6 + 14i + 4(-1) / 9 - (-1)
= 6 + 14i - 4 / 9 + 1
= 2 + 14i / 10
= (2/10) + (14/10)i
= 1/5 + (7/5)i

Comparing this simplified expression to the result you provided, we can see that it is not the same. Therefore, your answer of 6/7 + 5/7i is incorrect. Instead, the correct simplified expression is 1/5 + (7/5)i.