Let
- Verify that
is a root of . (1 marks)
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- List the other roots of
in polar form. (1 mark)
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- On the Argand diagram below, plot and label the points that represent all the roots of
. (2 marks)
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- i. On the Argand diagram below, sketch the ray that originates at the real root of
and passes through the point represented by . (1 mark)
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- ii. Find the equation of this ray in the form
, where , and is measured in radians in terms of . (1 mark)
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- Verify that the equation
can be expressed in the form -
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- i. Express
in the form , where . (1 mark)
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- ii. Given that
satisfies ,
use De Moivre's theorem to show that
-
-
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