Help?
1)
3i-10/8i-5
2)
11i^2+1/-12i-8
I assume you are meant to express #1 as a complex number in standard form: a+bi
to do that, it helps to express the given values in standard form:
(-10+3i)/(-5+8i)
Now, multiply top and bottom by -5-8i, because
(a+bi)(a-bi) = a^2 + b^2
(-10+3i)(-5-8i) = 50 + 80i - 15i - 24i^2 = 50 + 65i + 24 = 74+65i
(-5+8i)(-5-8i) = 25 + 84 = 109
So, the fraction is
74/109 + 65/1209 i
For #2, 11i^2 = -11, so it is just -10/(-8-12i)
= -10(-8+12i)/208
= (80 - 120i)/208
Thank YOU Very Much.
Help Please?
1.30√-25 x 8√-49
2. 6√-64 + 12√-36
3. 4√-13 - 6√-13
30√-25 x 8√-49 = 30*5i * 8*7i = 8400i^2 = -8400
6√-64 + 12√-36 = 6*8i + 12*6i = 120i
4√-13 - 6√-13 = (4-6)√-13 = -2√13 i
Sure, I can help you with those questions. Let's break down each question and find the answer step by step.
1) 3i - (10 / 8i) - 5
To simplify this expression, we'll combine like terms. We can start by dealing with the fraction:
10 / 8i = 10 / (8 * i)
Since the denominator contains a variable (i), we'll multiply the numerator and denominator by its conjugate to eliminate the imaginary number in the denominator:
(10 / (8 * i)) * (i / i) = (10 * i) / (8 * i * i) = (10i) / (-8) = -5i / 4
So, the expression becomes:
3i - (-5i / 4) - 5
Now, let's combine like terms:
3i + (5i / 4) - 5
We can combine the imaginary terms:
(3i + 5i) / 4 - 5
(8i) / 4 - 5
2i - 5
Therefore, the simplified expression is 2i - 5.
2) (11i^2 + 1) / (-12i - 8)
To solve this expression, let's start by simplifying the imaginary term:
i^2 = -1
Therefore:
(11 * (-1) + 1) / (-12i - 8)
Simplifying further:
(-11 + 1) / (-12i - 8)
-10 / (-12i - 8)
Now, let's rewrite the denominator by factoring out a common factor of 4 from both terms:
-10 / (4(-3i - 2))
Next, we can divide both the numerator and denominator by 2 to simplify further:
-5 / (2(-3i - 2))
Finally, we can simplify the denominator by factoring out a common factor of -1:
-5 / (-2(3i + 2))
So, the simplified expression is:
5 / (2(3i + 2))
And, if you prefer factoring out the -1 from the denominator:
-5 / (2(-1)(3i + 2))
-5 / (-2)(3i + 2)
5 / (2)(3i + 2)
Therefore, the simplified expression is 5 / (2)(3i + 2).