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.