Question

write 3(cos225 +isin225) in the form a + ib.

Answer 1

225 degrees rings a bell, no?

Answer 2

it is complex numbers

Answer 3

Not yet ;)
I meant that sin225 and cos225 are supposed to be well-known numbers: they have to do with the 45-45-90 degree triangle, with sides a, a and a√2. Does that ring a bell?

See image. Both sin225 and cos225 are: \[-\frac{ 1 }{ 2 }\sqrt{2}\]

Answer 4

you mean right angled triangle?

Answer 5

yeah

Answer 6

so you mean the angles should be in the first quadrant?

Answer 7

No, 225 is in the third quadrant. I only meant that in the 3rd quadrant you get the same values (just negative) as in the triangle with 45-45-90 degrees.

Answer 8

Therefore you now have \[3(-\frac{ 1 }{ 2 }\sqrt2+i \cdot -\frac{ 1 }{ 2 }\sqrt 2)\]And if you work out the brackets you're done.

Answer 9

Yeah I get you but that does not make any change.

Answer 10

Is your problem solved then?