Question

Put the following complex numbers in the form a+bi:
(4 − 5i) − (6 − 3i)

Answer 1

Distributive property:
(4-5i)-(6-3i) --> 4-5i-6+3i (distribute the negative sign as -1, neg. times .neg is positive)

Combine like terms:
-2i-2

Answer 2

that's all you have to do?

Answer 3

Yep, don't overthink it

Answer 4

what about
(b) (2 − 3i) · (4 + 5i)
(c)3 − 4i/6 + 8i
(d) (1 + i)^20

for b, willl the i^2 become a -1?

Answer 5

For (b) you would need to foil (First Outer Inner Last): (2-3i)(4+5i)

2(4)+2(5i)-3i(4)-3i(5i) --> 8+10i-12i-15i^2

Then combine like terms

Answer 6

i know but once you do that, since i^2 = -1 would you change it?
and could you give me a bit of assistance with d by any chance

Answer 7

You wouldn't need to do anyhting with the exponent as you canont solve for i with the informaiton available - your just combining like terms. -15i^2 is as far as you can go.

As for (d) since you cannot add 1 and i, just distribute the exponent: 1^20+i^20

Answer 8

ok thanks