Answer:
i) 28 - 30i
ii) 36 + 28i
Step-by-step explanation:
i) x = 6 + i ⇒2x = 2(6 + i) = 12 + 2i
z = 4 - 8i ⇒ 4z = 4(4 - 8i) = 16 - 32i
2x + 4z = (12 + 2i) + (16 - 32i) = 28 - 30i
ii) w = -1 + 5i and z = 4 - 8i
w × z = (-1 + 5i)(4 - 8i) = -4 + 8i + 20i - 40⇒collect like terms
w × z = -4 + 28i - 40
∵
∴w × z = -4 + 28i - 40(-1) = -4 + 28i + 40 = 36 + 28i
Answer:
Step-by-step explanation:
The smallest side of a triangle is formed by the smallest angle in the triangle.
To find the side opposite (formed by) the 20 degree angle, we can use the Law of Cosines. The Law of Cosines states that for any triangle, , where
,
, and
are the three sides of the triangle and
is the angle opposite to
.
Let be the side opposite to the 20 degree angle.
Assign variables:
Substituting these variables, we get:
Therefore, the shortest side of this triangle is 3.5.