Given that Z¹=4+3i and Z²=2+3i.find z¹_ z²
To find z¹ * z², we simply multiply the real and imaginary parts of the two complex numbers separately and then combine them.
z¹ * z² = (4+3i) * (2+3i)
Using FOIL (First, Outer, Inner, Last):
(4+3i) * (2+3i)
= (4 * 2) + (4 * 3i) + (3i * 2) + (3i * 3i)
= 8 + 12i + 6i + 9i²
Remember that i² is equal to -1, so substituting that:
8 + 12i + 6i + 9i²
= 8 + 18i + 9(-1)
= 8 + 18i - 9
= -1 + 18i
Therefore, z¹ * z² = -1 + 18i.