Find u*v, if u=13j and v=i+3j
a.-39
b.39
c.(0,39)
d(1,39)
I expect you want the dot product, since the cross product will have a k component, and no choice does.
u=0i+13j and v=1i+3j
so, u•v = 0*1 + 13*3 = ...
u= 0i + 13j and v= 1i + 3j
u*v = (0*1) + (13*3)
= 0 + 39
= 39
So, the correct answer is B. 39
To find the product of two complex numbers, u and v, we can use the distributive property.
Given:
u = 13j
v = i + 3j
To find the product (u * v), we can multiply each term of u by each term of v:
(u * v) = 13j * (i + 3j)
Using the distributive property, we get:
(u * v) = 13j * i + 13j * 3j
Now let's evaluate each term separately:
13j * i:
Multiplying a complex number with a real number gives the same complex number:
13j * i = 13i * j
Since i * j = -j (due to the definition of imaginary unit), we can substitute:
13j * i = 13i * (-j)
Using the commutative property of multiplication, we get:
13j * i = -13i * j
Now let's evaluate the second term:
13j * 3j:
When multiplying two complex numbers, we multiply the real parts together and the imaginary parts together:
13j * 3j = (13 * 3) * (j * j)
Using the property that j * j = -1 (due to the definition of imaginary unit), we can substitute:
13j * 3j = (13 * 3) * (-1)
Simplifying further:
13j * 3j = -39
Now let's add the two terms together to find (u * v):
(u * v) = -13i * j + (-39)
Combining like terms, we get:
(u * v) = -13i * j - 39
Therefore, the answer is option a) -39.
u*v is not the usual notation for vectors
Are you finding the dot product or the cross product?
What is your choice of answer?