# Imaginary Numbers - Further MathsWatch

#1
The question is....

Write in the form 'a+ib' where a and b are any real number:

4( cos (-5pi/6) + i sin (-5pi/6))

The answer in the book is:

-2 rt3 - 2i

Any help would be brilliant and I've spent about half an hour trying to figure this one out and I've just ended up getting myself more confused than when I started!!
0
4 years ago
#2
(Original post by amydowse)
The question is....

Write in the form 'a+ib' where a and b are any real number:

4( cos (-5pi/6) + i sin (-5pi/6))

The answer in the book is:

-2 rt3 - 2i

Any help would be brilliant and I've spent about half an hour trying to figure this one out and I've just ended up getting myself more confused than when I started!!
type the cosine and the sine in the calculator (in radians)
then multiply by 4
0
4 years ago
#3
(Original post by amydowse)
The question is....

Write in the form 'a+ib' where a and b are any real number:

4( cos (-5pi/6) + i sin (-5pi/6))

The answer in the book is:

-2 rt3 - 2i

Any help would be brilliant and I've spent about half an hour trying to figure this one out and I've just ended up getting myself more confused than when I started!!
Look at the form it's currently in: after you bring the four into the bracket, you get 4cos(-5pi/6) + i(4sin(-5pi/6)). Can you see that's exactly of the form a+bi? cos and sin are always going to be real when you put real numbers into them, so all you need to do is evaluate what the cosine and sine of -5pi/6 is.

Tip: learn the values of cosine and sine at the following values:
0, pi/6, pi/4, pi/3, pi/2, pi. From these, and making use of a sketch graph you can work out any of the other common values you'll need to evaluate. It's very useful to be able to immediately know what these things are without having to reach for a calculator every time.
0
4 years ago
#4
(Original post by amydowse)
The question is....

Write in the form 'a+ib' where a and b are any real number:

4( cos (-5pi/6) + i sin (-5pi/6))

The answer in the book is:

-2 rt3 - 2i

Any help would be brilliant and I've spent about half an hour trying to figure this one out and I've just ended up getting myself more confused than when I started!!
have you tried multiplying out the brackets, to get it in the form x+iy (rectangular form)?
0
#5
Thank you so much - I'd been doing a lot longer way!
I didn't realise I could just expand it (rather stupidly)
Thank you
0
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