Solution

36710

First name
Jordan Harun
School
St Stephen's School
Country
Age
15

1. Z_1 = 4 + 5i
Z_2 = 3 - 5i
Z_3 = 7 + 0i THEREFORE REAL

2. Z_1 = -6 + 3i
Z_2 = 6 + 3i
Z_3 = 0 + 6i THEREFORE IMAGINARY

3.a) FOR A REAL NUMBER: Z_1 = a + ib
Z_2 = a - ib
Z_3 = 2a + 0i THEREFORE REAL

3.b) FOR AN IMAGINARY NUMBER: Z_1 = a + ib
Z_2 = -a + ib
Z_3 = 0 + 2ib THEREFORE IMAGINARY

4. Z_1 = 1 + 2i
Z_2 = 1 - 2i
Z_3 = 5 + 0i THEREFORE REAL

5. Z_1 = 3 + 3i
Z_2 = 3 + 3i
Z_3 = 0 + 18i THEREFORE IMAGINARY

6.a) Z_1 = a + ib
Z_2 = a - ib
Z_3 = a^2 + b^2 THEREFORE REAL

6.b) Z_1 = a + ib
Z_2 = a + ib
Z_3 = a^2 + 2aib + b^2 (NUMBERS MUST BE ALL THE SAME)

e.g Z_1 = 3 + 3i
Z_2 = 3 + 3i
Z_3 = 0 + 18i THEREFORE IMAGINARY