Can you help me understand how to do this: write the complex number in the form a + bi. 8(cos 30° + i sin 30°)?

Hello!

First, we can open the parentheses using the distributive property:

8*(cos(30°) + i*sin(30°)) = 8*cos(30°) + i*(8*sin(30°)).

Formally, this is the answer already, because 8cos(30°) and 8sin(30°) are real numbers (which is required for the form a+ib). But we can simplify this if recall that sin(30°) = `1/2` and cos(30°) = `sqrt(3)/2.`

So the final answer is 8*(cos(30°) + i*sin(30°)) = `4sqrt(3)+4i.`

Hello!

First, we can open the parentheses using the distributive property:

8*(cos(30°) + i*sin(30°)) = 8*cos(30°) + i*(8*sin(30°)).

Formally, this is the answer already, because 8cos(30°) and 8sin(30°) are real numbers (which is required for the form a+ib). But we can simplify this if recall that sin(30°) = `1/2` and cos(30°) = `sqrt(3)/2.`

So the final answer is 8*(cos(30°) + i*sin(30°)) = `4sqrt(3)+4i.`