Final answer:
To express 3 cis(-30) in rectangular form, you multiply 3 by cosine and sine of -30 degrees to get 3√3/2 - 3i/2, which combines the real and imaginary components.
Step-by-step explanation:
To express 3 cis(-30) in rectangular form, we utilize Euler's formula which states that cis(θ) is equivalent to cos(θ) + i*sin(θ), where i is the imaginary unit. The angle -30 degrees is in the fourth quadrant of the unit circle where the cosine is positive and the sine is negative.
The rectangular form of 3 cis(-30) is obtained by multiplying 3 by the cosine and sine of -30 degrees respectively:
- cos(-30) = √3/2
- sin(-30) = -1/2
Thus, the rectangular form is:
3 * (√3/2 + i*(-1/2))
= 3√3/2 - 3i/2
This gives us the complex number in rectangular form with a real part of 3√3/2 and an imaginary part of -3i/2.