Pre Calc Please Explain

Question

Use the numbers x=3+2i, w=2−i, z=−2+3i to compute the following. (Round to two places as needed.)

x−2w=

x^2=

x/w=

(inverse w) w⋅w¯¯¯¯ =

Answer 1

For complex numbers you need to know this:

i = √-1

i² = -1

i³ = -i

i⁴ = 1

i⁵ = i ...... and so on. The cycle repeats. The algebra becomes straight forward when you know these facts. Go ahead and try.

You also need to know about the conjugate. The conjugate of a + bi is a - bi. Multiplying by the conjugate removes the complex portion of the number. Try it out and see.

For x/w you need to multiply numerator and denominator by the conjugate of w. Try it for yourself!

Send your work and then we can take it from there.