Question

using de Moivre's theorem to find (1-i)^6 in the form a+bi
(begin by expressing 1-i in pola forms)

Answer 1

do u know how to find the polar form of a complex number?

Answer 2

no, i havent learnt it yet

Answer 3

if \(z=a+ib\), its polar form is
\[\large z=\rho(\cos\theta+i\sin\theta) \]
where \(\rho=|z|=\sqrt{a^2+b^2}\) and \(\theta\) is the angle between the positive x-axis and the vector \(z\).

Answer 4

so
\[\large \rho=\sqrt{1^2+(-1)^2}=\sqrt{2} \]

Answer 5

the angle (argument) can be measured either counterclockwise or, clockwise if z is in the III or IV quadrants or counterclockwise if < is in the I or II quadrants.

how were u taught to do this?

Answer 6

* z not <