what is 7-2i in trig form?
and
if u=3j and v=7i+j
what is the dot product of u times v
don't get this one because there are no i terms for u
thanks
I am not sure what you mean by the "trig form" of a complex number. The magnitude is sqrt(7^2 + 2^2) = sqrt53
The complex unit vector is e^(i*theta)
where theta = arcsin(-2/7) - -16.6 degrees or -0.29 radians
Thus 7 -2i = sqrt53*e^-0.29i
In the second questiuon, you seem to be talking about two-dimensional vectors, not complex numbers
The dot product is
u*v = 7*0 + 3*1 = 3
Here is a nice webpage that shows how to do the first one, just follow their example #1 with your number.
For some strange reason, they use j instead of i to represent the complex component of the number.
As for your second question , how about
u = 0i + 3j, now you have an i-term.
silly me, forgot to include the link
http://www.intmath.com/complex-numbers/4-polar-form.php
To find the trigonometric form of a complex number, we need to express it as a combination of a magnitude and an angle.
For the complex number 7 - 2i, we can calculate its magnitude (r) and angle (θ) using the following formulas:
Magnitude (r) = √(a^2 + b^2)
Angle (θ) = arctan(b/a)
In this case, a = 7 (real part) and b = -2 (imaginary part). So, let's calculate the magnitude and angle:
Magnitude (r) = √(7^2 + (-2)^2) = √(49 + 4) = √53
Angle (θ) = arctan((-2)/7) ≈ -0.2793 (in radians)
Therefore, the trigonometric form of 7 - 2i is approximately √53 * (cos(-0.2793) + i * sin(-0.2793)).
Now, let's move on to the second question about the dot product:
Given u = 3j and v = 7i + j, we can calculate the dot product using the formula:
Dot product (u · v) = (u_x * v_x) + (u_y * v_y)
In this case, u has no x-component (i term) and v has no y-component (j term). The dot product formula becomes:
Dot product (u · v) = (0 * 7) + (3 * 1) = 0 + 3 = 3
Therefore, the dot product of u and v is 3.