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!!!
DEF is shown in the attachment.
Answer: x = 36.08
Step-by-step explanation: We can use <u>Law</u> <u>of</u> <u>Sines</u> to determine x, which is written as:
where
F is the angle at vertex F
The angle is calculated knowing that the sum of all internal angles of a triangle is 180°:
F + 49 + 90 = 180
F + 139 = 180
F = 180 - 139
F = 41
Then, Law of Sines will be:
Sin(90) = 1
sin (41) = 0.6560
Substituing and rearraging:
x = 36.08
<u>The value of x is 36.08 units</u>
Answer:
(-1, 5)
Step-by-step explanation:
3 [x + y = 4]
3x + 3y = 12
- 3x + 7y = 32
-4y = -20
y = 5
x + 5 = 4
x = -1
Answer:
83/6=13.84 and 15/2=7.5
Step-by-step explanation:
X-2y = 3
-2y=3-x move the x over to the other side
-y=3/2 -1/2x divide both sides by 2
y=1/2x - 3/2 divide both sides by -1