Question

Choose the polar form of the complex number -1 + i.

Answer 1

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Answer 2

idk srry

Answer 3

its ok

Answer 4

I'm no help sorry

Answer 5

So, doing some recheck on the theory, you know that any complex number represents a vector in a complex referential system, so any expression in that form can be represented as:
\[ \vec{Z} = a+bi\]
so therefore, the module or the "magnitude" of the vector is given by the equation:
\[\left| \vec{z} \right|= \sqrt{a ^2 + b^2}\]
and the angle it has referential to the x- axis or the "real" component is calculated by:
\[arctg(\left| \vec{z} \right|) = \theta \]
and that can be used to describe the vector at it´s polar form:
\[\left| \vec{z} \right|_{\theta}\]

Answer 6

So, taking the complex number:
\[ \vec{z} = -1+i\]
we find it's module:
\[\left| \vec{z} \right|= \sqrt{(-1)^2 + (1)^2}\]
\[\left| \vec{z} \right| = \sqrt{2}\]
And now, the angle:
You'd have to represent it right now, but I'll do it without a representation and leave that to you.
well, the formula was:

\[arctg(\left| \vec{z} \right|)= \theta\]
So:
\[\tan \theta = \left| \vec{z} \right|\]
that ould mean:
\[Tan \theta = \frac{ 1 }{ -1 } = -1\]
so therefore:
\[\theta = 135\]
and transfering that to polar form:
\[\sqrt{2}_{135}\]