Convert the complex number c=3cis 0.25 into rectangular form.
(x,y) = (3cos .25, 3sin .25)
To convert a complex number from polar form to rectangular form, we can use the formulas:
Re(c) = r * cos(theta)
Im(c) = r * sin(theta)
Given the complex number c = 3cis(0.25),
- The magnitude (r) is 3
- The angle (theta) is 0.25
Using these values:
Re(c) = 3 * cos(0.25)
Im(c) = 3 * sin(0.25)
Now, let's calculate:
Re(c) ≈ 3 * 0.97 ≈ 2.91
Im(c) ≈ 3 * 0.25 ≈ 0.75
Therefore, the rectangular form of the complex number c=3cis(0.25) is approximately 2.91 + 0.75i.