Question

(5-i)^2-(4+i)(4-i)

Answer 1

do you know FOIL ? or how to multiply two binomials
?

Answer 2

yes

Answer 3

can you help me though?

Answer 4

First step, expand
(5-i)^2

what do you get ?

Answer 5

(5-i)(5-i)

Answer 6

which is 25-5i-5i-1

Answer 7

which is 25-5i-5i-1
yes, where you changed +i^2 into -1
you can combine -5i - 5i into -10i

and 25-1 is 24
so
(5-i)^2 = 24 -10i

Answer 8

now do
-(4+i)(4-i) which is -1 * (4+i)*(4-i)

I would do (4+i)(4-i) and after I get the answer, multiply every term by -1

Answer 9

(16-4i+4i+1)

Answer 10

yes, but that simplifies to what ?

Answer 11

17?

Answer 12

yes, but don't forget we started with
-(4+i)(4-i)

Answer 13

so -17

Answer 14

25

Answer 15

24-10i-17

Answer 16

yes. putting it together we have
(5-i)^2-(4+i)(4-i) = 24 -10i -17
simplify to get the final answer

btw, notice (4+i)(4-i) is multiply *complex conjugates*
a complex conjugate has the imaginary part multiplied by -1
you will get a real number (we got 17) if you multiply complex conjugates

Answer 17

7-10i

Answer 18

it looks like you know how to do these problems

Answer 19

thank you