College Algebra

Question

1 a) Evaluate: 15i - (3 + 2i) -11

 

b) Evaluate: (5 - i) (3 + 4i)

 

c) Evaluate: i^60

Answer 1

1a)

 

15i - (3 + 2i) - 11 = ?

 

Distribute, then combine all real terms together, and all imaginary terms together:

 

15i - (3 + 2i) - 11 = 15i - 3 - 2i - 11

 

= (-3 - 11) + (15 - 2)i = -14 + 13i

 

1b)

 

(5 - i) (3 + 4i) = 5(3 + 4i) - i(3 + 4i) = 15 + 20i - 3i - 4i²

 

Remember i² = -1, so -4i² = -4(-1) = 4

 

(5 - i) (3 + 4i) = (15 + 4) + (20 - 3)i = 19 + 17i

 

1c)

 

i⁶⁰ = ?

 

Are you familiar with the formula e^ix = cos(x) + i sin(x) ?

 

I will use it here:

 

i = 0 + 1i = cos(π/2) + i sin(π/2) = e^iπ/2

 

i⁶⁰ = (e^iπ/2)⁶⁰ = e^{(60 * iπ/2)} = e^i30π = cos(30π) + i sin(30π) = 1 + 0i = 1