Question

Find each power. Express the result in rectangular form. (1-i)^5

Answer 1

rewrite it in this way

(1-i)^5 = (1-i)^2 *(1-i)^3

for (1-i)^2 = ? hope you know thie formula (a-b)^2 = ?
for (1-i)^3 = ? hope so you know formula (a-b)^3 = ?

just use these formule and will get the right answer sure

but ATTENTION on i^2 = -1

Answer 2

(-4, 4) Expand using binomial theorem, combine like terms, and find the real and imaginary parts resulting from the equation -4+4i

Answer 3

pardon me i don't know the formulas

Answer 4

@jhonyy9 what do you do after you break the equation

Answer 5

You can use binomial theorem or you can use demorive theorem

Answer 6

write in polar form if you want to use demorive theorem

Answer 7

im just having trouble with the first steps, I know what r equal but i don't know how

Answer 8

\[z=a+bi \\ r=|z|=|a+bi|=\sqrt{a^2+b^2}\]

Answer 9

so would it be \[\sqrt{1^{2+-i ^{2}}}\]

Answer 10

I don't know how you got that from what I wrote :p
\[\text{ Solve } \tan(\theta)=\frac{b}{a} \text{ keeping in my that } \theta \text{ needs to be in the } \\ \text{ quadrant your point is in}\]

Answer 11

a=1 and b=-1 just plug them in

Answer 12

how did you get -1?, sorry math isn't my thing

Answer 13

just by looking at 1-i

Answer 14

1-i is the same as 1-1i
comparing this to a+bi
I see a is 1 and b is -1

Answer 15

ohh, now I understand, Thank You

Answer 16

np