x * 2y = -4 - 32i
x - y = -6 - 5i
3y - 2x = 16 + 12i
Step-by-step explanation:
x = -2 - 3i
y = 4 + 2i
Note: Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.
a) x * 2y = (-2 - 3i) × 2(4 + 2i)
= (-2 - 3i) × (8 + 4i)
= -2(8 + 4i) - 3i(8 + 4i)
= -16 - 8i - 24i - 12(i²)
Recall in complex numbers: i² = -1
= -16 - 8i - 24i - 12(-1) = -16 - 8i - 24i +12 = -16 + 12- 8i - 24i
x * 2y = -4 - 32i
b) x - y = -2 - 3i - (4 + 2i) = -2 - 3i -4 - 2i
x - y = -2 - 4 -3i - 2i
x - y = -6 - 5i
c) 3y - 2x = 3(4 + 2i) - 2(-2 - 3i)
= 12 + 6i + 4 + 6i = 12 + 4 + 6i + 6i
3y - 2x = 16 + 12i