Complex Number

Question 1

U = - 1 + (4 root 3) i.

Find 2 square root of u.

Answer 1

Root u =
root - 1 + (4 root 3) i = x + y i.
- 1 + (4 root 3) i = (× + yi) square.
= x square + 2xyi - y square.

Compare: x square - y square = -1.
2xy = 4 root 3.

Solve simultaneously:
x = + or - root 3, y = + or - 2.
+ or - (root 3 + 2i).

Question 2

U = -1+(4 root 3)i
Sketch l z-u l = 1.
Find greatest value of org z.

Answer 2

Move the centre from origin to u.
A bi tangent form between origin and centre.

From tan angle = 1/ 3 root 4 find angle.
Angle multiply 2.

Answer + pai/2.
Get angle at origin from x axis.