Rewrite the complex number in rectangular form, a + bi.

Question

Rewrite the complex number in rectangular form, a + bi.

 

z=7cis(pi/6)=?

 

A. 7+7i

B. ((7(sqrt 3))/2)+(7/2)i

c. (sqrt 3/2)+(1/2)i

D. (7/2)+(7/2)i

Answer 1

To rewrite a complex number from cis form to rectangular form, we can use:

rcis(θ) = r(cos(θ) + isin(θ))

Given that z = 7cis(π/6), we can convert it into the rectangular form:

z = 7(cos(π/6 + isin(π/6))

To evaluate this, we can use unit circle values since we know:

cos(π/6) = √3/2 and sin(π/6) = 1/2

So, we can substitute them into the equation:

z = 7(√3/2 + (1/2)i) We can distribute the 7

z = (7√3)/2 + (7/2)i

So, the correct answer is B.

Answer 2

z = 7[cos(π/6) + i sin(π/6)]

 

cos(π/6) = (√3)/2

 

sin(π/6) = 1/2

 

z = 7[(√3)/2 + i(1/2)]

 

z = 7(√3)/2 + (7/2)i

 

The correct answer is (B).