change 8 cis 240 degrees to rectangular form
x = rcosθ = (8)(-1/2) = -4
y = rsinθ = 8(-√3/2) = -4√3
so, 8cis240° = -4 - 4√3 i
8 cis 240°
= 8(cos 240° , i sin240°
= 8(-1/2 , -√3/2)
= (-4 , -4√3)
To change a complex number expressed in polar form (cis) to rectangular form, you can use the trigonometric functions cosine and sine.
Here's how to convert 8 cis 240 degrees to rectangular form:
Step 1: Represent the angle in radians
240 degrees can be converted to radians by multiplying it by π/180. So, 240 degrees = 240 * π/180 = 4π/3 radians.
Step 2: Write the rectangular form
In rectangular form, a complex number is expressed as a sum of its real and imaginary parts.
The formula for a complex number in rectangular form is:
z = x + yi
Step 3: Calculate the real and imaginary parts using cosine and sine
The real part (x) is calculated by multiplying the modulus (8 in this case) with the cosine of the angle.
The imaginary part (y) is calculated by multiplying the modulus with the sine of the angle.
So, for 8 cis 240 degrees:
x = 8 * cos(4π/3)
y = 8 * sin(4π/3)
Step 4: Simplify the expression
Using a calculator to evaluate the cosine and sine values, we have:
x = 8 * (-0.5) = -4
y = 8 * (√3/2) = 4√3
Therefore, 8 cis 240 degrees in rectangular form is -4 + 4√3i.