Question

(a+bi)^2=i
What is square(i)
solve geometrically in a complex number plane

Answer 1

\[ i= \sqrt{-1} \]
what is
\[ \sqrt{-1}\sqrt{-1} \]

Answer 2

1

Answer 3

you cant

Answer 4

no. by definition sqrt(a)*sqrt(a)= a
so sqrt(-1)*sqrt(-1)= -1

Answer 5

ok

Answer 6

how do i solve this question with the complex number plane?

Answer 7

I see how to do it algebraically. But I'm thinking about how to do it geometrically
Did they give you any clues?

Answer 8

Scetch images in a complex number plane. If that is of any help

Answer 9

In the complex plane, the number i is represented by the ordered pair (0,1) or the polar form (1, pi/2). If we take the square root of this, we will take the square root of the radius (conveniently still one) and half the angle (it becomes pi/4). That gives the polar coordinate (1,pi/4), which converts to the Cartesian form (sqrt2/2,sqrt2/2). Keep in mind there will be two roots, so the second will be symmetric on the plane (-sqrt2/2,-sqrt2/2).