Help?
I Kind of understand this , but still I am stuck.
1. (2+4i)/3-i
2. 3√-50 + -72
3.(-4+√-15)^2
4.-4+√-20
5.7√-2(-4√-3)
we kind of don't know where you get stuck. Show us what you got, and we can help you work it the rest of the way.
1. I got 6+3/10
but i don't believe that's the correct answer.
2. i got √21.21+√-8.49
3. i got 34+14√10i
4. i got -1+√5i
#1: (2+4i)/(3-i)
= (2+4i)(3+i) / (3-i)(3+i)
= (6 + 12i + 2i + 4i^2) / (3^2 - i^2)
= (6 + 14i - 4) / (9+1)
= (2+14i)/10
= 1/5 + 7/5 i
#2: 3√-50 + -72
3√50 i - 72
3*5√2 i - 72
-72 + 15√2 i
in this kind of exercise, there's no call to approximate √ values with decimals. The √ is exact; the decimals are only an approximation.
#3: (-4+√-15)^2
= (-4 + √15 i)^2
= (-4)^2 + 2(-4)(√15 i) + (√15 i)^2
= 16 - 8√15 i - 15
= 1 - 8√15 i
#4: -4+√-20
= -4 + √20 i
= -4 + 2√5 i
#5: 7√-2(-4√-3)
= 7(√2 i)(-4)(√3 i)
= -28 √6 i^2
= 28√6
Does that help? Just take these things step by step, keeping track of the i's and signs.
I'd be happy to help!
1. To simplify (2+4i)/(3-i), we can use a technique called complex conjugate. Multiply the numerator and the denominator by the conjugate of the denominator, which is (3+i).
(2+4i) * (3+i) / (3-i) * (3+i)
Simplify the numerator: 6 + 2i + 12i + 4i^2
Simplify the denominator: 9 - 3i + 3i - i^2
Remember that i^2 is equal to -1, so:
6 + 14i + 4(-1) / 9 - (-1)
Simplify further:
6 + 14i - 4 / 9 + 1
Combine like terms:
2 + 14i / 10
Divide numerator and denominator by 2:
1 + 7i / 5
Therefore, the simplified form of (2+4i)/(3-i) is (1+7i)/5.
2. To simplify 3√-50 + -72, we need to evaluate the square root of -50 first. Since the square root of -50 is an imaginary number, we will express it in terms of "i".
sqrt(-50) = sqrt(-1*25*2) = i * 5 * sqrt(2)
Now we can rewrite the expression:
3 * i * 5 * sqrt(2) - 72
Simplify:
15i * sqrt(2) - 72
This is the simplified form of the expression.
3. To simplify (-4+√-15)^2, we can use the FOIL method. First, square the terms inside the parentheses:
(-4)^2 + 2*(-4)*√(-15) + (√(-15))^2
Simplify:
16 - 8√(-15) + (-1)(15)
Since √(-1) is equal to "i", we can rewrite the expression:
1 + 16 - 8i√15
Combine like terms:
17 - 8i√15
This is the simplified form of (-4+√-15)^2.
4. To simplify -4+√-20, we first need to find the square root of -20. Expressing it in terms of "i":
√(-20) = √(-1*4*5) = 2√5 * √(-1)
Rewrite the expression:
-4 + 2√5 * √(-1)
Simplify:
-4 + 2√5 * i
This is the simplified form of -4+√-20.
5. To simplify 7√-2(-4√-3), we can use the distributive property. Multiply the terms inside the square root:
7 * √(-2) * (-4) * √(-3)
Simplify:
-28 * √2 * √3
Combine the square root terms:
-28 * √(2 * 3)
Simplify further:
-28 * √6
This is the simplified form of 7√-2(-4√-3).