Answer:
see explanation
Step-by-step explanation:
Note that
• i² = - 1
The standard form of a complex number is
• a + bi ( a is the real part and b the imaginary part
1
3i(2 - 8i) ← distribute parenthesis by 3i
= 6i - 24i²
= 6i - 24(- 1)
= 24 - 6i
2
(- 4 - 9i)(5 + 8i) ← expand using FOIL
= - 20 - 32i - 45i - 72i²
= - 20 - 77i - 72(- 1)
= - 20 - 77i + 72
= 52 - 77i
3
(7 - 2i)(7 + 2i) ← expand using FOIL
= 49 + 14i - 14i - 4i²
= 49 + 0 - 4(- 1)
= 49 + 4
= 53 ← a real number
4
(6 + 5i)²
= (6 + 5i)(6 + 5i) ← expand using FOIL
= 36 + 30i + 30i + 25i²
= 36 + 60i + 25(- 1)
= 36 + 60i - 25
= 11 + 60i
