Express the number in rectangular form.
3(cosπ/3+isinπ/3)
cos pi/3 = 1/2
sin pi/3 = sqrt 3/2
so x = 3/2 and y = (3/2)sqrt 2
To express a number in rectangular form, we need to rewrite it in the form a + bi, where a and b are real numbers.
The given number is in polar form, which is expressed as r(cosθ + isinθ), where r is the magnitude of the number and θ is its argument.
In this case, the given number is 3(cosπ/3 + isinπ/3).
We can start by evaluating cos(π/3) and sin(π/3). Recall that cos(π/3) = 1/2 and sin(π/3) = √3/2.
Now we can substitute these values in:
3(cosπ/3 + isinπ/3) = 3(1/2 + i√3/2)
Distributing the 3:
= 3/2 + 3i√3/2
Now we have expressed the given number in rectangular form as a + bi:
3(cosπ/3 + isinπ/3) = 3/2 + 3i√3/2