Question

Using argend plane, interpret geometrically, the meaning of i=√-1 and its integral powers.​

Answer 1

i=√-1 and its integral powers.​

Step-by-step explanation:

• i, i², i³ and i^4  namely i, -1 , -i, 1 as A,B,C and D.

• We can notice this when we multiply a number of times in a row

• i by i, the result by i and repeat.

• The point A is rotated in an anticlockwise direction through pi/2. As a result, A becomes B, B becomes C, C becomes D, and D becomes A.

• complex number z =re^ix
• B = i(z) = e^i(pi/2).re^ix = re^i(x+pi/2).

• We can see that OB = OA = r, and B's argument has grown by pi/2. As a result, OB is obtained by rotating OA around the origin in the anticlockwise direction through pi/2.

Thus, multiplying a complex number z by I indicate rotating that point 'z' in the plane 90 degrees clockwise around the origin.

Answer 2

Answer:

Geometrical representation of

$i \: = \sqrt{ - 1}$