write 2=5cis 11pie/6 in standard form.
Your question makes no sense to me as written but
2 = 5 cos 11 pi/6 + 5 i sin 11 pi/6
= 5 e^i(11 pi/6)
12 pi/6 = 2 pi is a full circle
11 pi/6 is a full circle - pi/6
2/5 = cos (12 pi/6 -pi/6) + i sin(12 pi/6 - pi/6)
2/5 = cos (-pi/6) + i sin (-pi/6)
2/5 = +sqrt (3)/2 - i/2
I'm not sure if the answer's a) 5sqrt3/2-5/2i b) 5sqrt3/2+5/2i c) -5sqrt3/2-5/2i d) -5sqrt3/2+5/2i
check for typo why do you have 2 on the left
if you had x and not 2 on the left it would be a
Okay thanks so much! that's right
To convert a complex number from polar form to standard form, we can use the formula:
a + bi = r(cosθ + isinθ)
where a + bi is the standard form of the complex number, r is the magnitude or modulus of the complex number, θ is the argument or angle of the complex number.
In the given complex number, 2 = 5cis(11π/6), we have:
- The magnitude, r = 5,
- The argument, θ = 11π/6.
To convert it to standard form, we substitute these values into the formula:
2 = 5(cos(11π/6) + isin(11π/6))
Now, let's evaluate the trigonometric functions for the given angle:
cos(11π/6) = cos(π + π/6) = -cos(π/6) = -√3/2
sin(11π/6) = sin(π + π/6) = -sin(π/6) = -1/2
Substituting these values back into the formula:
2 = 5*(-√3/2 + (-1/2)i)
Now, let's simplify:
2 = -5√3/2 - 5/2 i
Finally, we multiply every term in the expression by 2 to eliminate the denominator:
4 = -5√3 - 5i
Therefore, the complex number 2 = 5cis(11π/6) in standard form is 4 = -5√3 - 5i.