Answer: A is first
Step-by-step explanation:
Answer:
irrational.
Step-by-step explanation:
√3 is irrational.
product of rational and irrational number is always irrational.
6×√3=6√3
So, 4/3 - 2i
4/3 - 2i = 12/13 + i8/13
multiply by the conjugate:
3 + 2i/3 + 2i
= 4(3 + 2i)/(3 - 2i) (3 + 2i)
(3 - 2i) (3 + 2i) = 13
(3 - 2i) (3 + 2i)
apply complex arithmetic rule: (a + bi) (a - bi) = a^2 + b^2
a = 3, b = - 2
= 3^2 + (- 2)^2
refine: = 13
= 4(3 + 2i)/13
distribute parentheses:
a(b + c) = ab + ac
a = 4, b = 3, c = 2i
= 4(3) + 4(2i)
Simplify:
4(3) + 4(2i)
12 + 8i
4(3) + 4(2i)
Multiply the numbers: 4(3) = 12
= 12 + 2(4i)
Multiply the numbers: 4(2) = 8
= 12 + 8i
12 + 8i
= 12 + 8i/13
Group the real par, and the imaginary part of the complex numbers:
Your answer is: 12/13 + 8i/13
Hope that helps!!!
Answer:
(4, -6), (-10, -6), (-3, 1), (-3, -13)
Step-by-step explanation:
If we add/subtract t to/from any x/y coordinate, we will form a line segment with length 7. Hence, (4, -6), (-10, -6), (-3, 1), (-3, -13).
We know the area of the middle rectangle is 48 (length * width). removing that rectangle leaves us with two semicircles. you can combine those semicircles to be the equivalent of one circle. the area for a circle is r^2 * pi. we know the diameter is 4 because that is where we cut the semicircles. radius is half the diameter, so r is 2. 2^2 is 4, 4* pi is 12.56. add 12.56 (area of semicircles) with 48 (area of rectangle) and we get 60.56
