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# Further Maths Complex Numbers watch

1. z = 6 ( Cos (5π/6) + isin(5π/6) )
w = 4 (Cos (-π/4) +isin(-π/4) )

Write the following complex numbers in the form r (cosθ+isinθ),
where r > 0 and -π < θ ≤ π

i) z/w
ii) w/z
2. (Original post by 98701)
z = 6 ( Cos (5π/6) + isin(5π/6) )
w = 4 (Cos (-π/4) +isin(-π/4) )

Write the following complex numbers in the form r (cosθ+isinθ),
where r > 0 and -π < θ ≤ π

i) z/w
ii) w/z
What have you tried? Post your working.
3. (Original post by 98701)
z = 6 ( Cos (5π/6) + isin(5π/6) )
w = 4 (Cos (-π/4) +isin(-π/4) )

Write the following complex numbers in the form r (cosθ+isinθ),
where r > 0 and -π < θ ≤ π

i) z/w
ii) w/z
i . your modulus is just 6 / 4 which is r in modulus arg form
your argument is 5n/6 - n/4

ii. same method just switch numbers around
4. (Original post by Tbarker1)
i . your modulus is just 6 / 4 which is r in modulus arg form
your argument is 5n/6 - n/4

ii. same method just switch numbers around
That is what i got but is 5n/6 - n/4 a principle argument?
5. (Original post by 98701)
That is what i got but is 5n/6 - n/4 a principle argument?
yeah its the argument you place after cos( and isin(
6. (Original post by Tbarker1)
yeah its the argument you place after cos( and isin(
Ok, Thanx
7. Another way is to convert z and w into exponential form and (z/w) and (w/z) can then be easily tranformed back into the modulus and argument form.

Or note that:

Can you take this forward?
8. (Original post by simon0)
Another way is to convert z and w into exponential form and (z/w) and (w/z) can then be easily tranformed back into the modulus and argument form.

Or note that:

.

Can you take this forward?
should be able to
Thank you \(^o^)/
9. i) 6/4(Cos(13/12 π)+iSin(13/12 π))
θ > π so -2π to give:
6/4(Cos(-11/12 π)+iSin(-11/12π))

ii)4/6(Cos(-13/12 π)+iSin(-13/12 π))
θ < π so + 2π to give:
4/6(Cos(11/12 π)+iSin(11/12 π))
10. (Original post by physconomics)
i) 6/4(Cos(13/12 π)+iSin(13/12 π))
θ > π so -2π to give:
6/4(Cos(-11/12 π)+iSin(-11/12π))

ii)4/6(Cos(-13/12 π)+iSin(-13/12 π))
θ < π so + 2π to give:
4/6(Cos(11/12 π)+iSin(11/12 π))
Thank you :^_^:

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