-(2%2B4i).jpeg "(5+3i) (2+4i)")
Multiplying Complex Numbers: (5 + 3i)(2 + 4i)
This article will guide you through the process of multiplying two complex numbers, (5 + 3i) and (2 + 4i).
Understanding Complex Numbers
Complex numbers are expressed in the form a + bi, where:
- a represents the real part.
- b represents the imaginary part.
- i is the imaginary unit, where i² = -1.
Multiplying Complex Numbers
To multiply two complex numbers, we use the distributive property, just like with regular binomials:
(5 + 3i)(2 + 4i) = 5(2 + 4i) + 3i(2 + 4i)
Next, we distribute each term:
= (5 * 2) + (5 * 4i) + (3i * 2) + (3i * 4i)
Simplifying the multiplication:
= 10 + 20i + 6i + 12i²
Remember that i² = -1. Substitute this value:
= 10 + 20i + 6i + 12(-1)
Combining like terms:
= (10 - 12) + (20 + 6)i
Finally, we arrive at the product:
= -2 + 26i
Therefore, the product of (5 + 3i) and (2 + 4i) is -2 + 26i.