Question

PLZ ANSWER FAST ....WHAT IS THE POLAR FORM OF -1+i ?????????​

Answer 1

Answer:

-1 + i = √2 exp ( 3 π i / 4 )

       = √2 cis ( 3 π / 4 )

Step-by-step explanation:

Let's put z = -1 + i.

Its norm is |z| = √( 1² + 1² ) = √2.

Plotting on a diagram, it is in the upper left quadrant, making a 135° with the positive x-axis.  Remembering that π corresponds to half way around the circle (i.e. 180°), this is 135/180 = 3/4 of the way there, so the argument is 3π/4.

[ More formally, tan θ = 1 / -1 = -1, so θ is 3π/4 or -π/4.  Since the real part Re(z) = -1 is negative, we conclude that θ = 3π/4.  A diagram is easier.  ]

So

z = √2 exp ( 3 π i / 4 )