Question

Please help! Change 2(cos210 degrees+isin210 degrees) to rectangular (algebraic) form.
a. -1+isqrt3
b. -1-isqrt3
c. -sqrt3+i
d. -sqrt3-i

Answer 1

Hint:

x = r*cos(theta)

y = r*sin(theta)

Answer 2

if you let the y axis be the imaginary axis, then the number x+y*i represents the point (x,y) in the cartesian plane

Answer 3

:/ Can you help me solve it step by step?

Answer 4

Let me do a similar example and hopefully that will help

Answer 5

Example

Change 3(cos60 degrees+isin60 degrees) to rectangular (algebraic) form.

Answer 6

In this example, r = 3 and theta = 60

Answer 7

So

x = r*cos(theta)

x = 3*cos(60)

x = 3*(1/2)

x = 3/2

---------------

and

y = r*sin(theta)

y = 3*sin(60)

y = 3*(sqrt(3)/2)

y = (3/2)*sqrt(3)

Which means

3(cos60 degrees+isin60 degrees)

converts to

3/2 + (3/2)*sqrt(3)*i