(2-3i)-state-the-value-of-a-and-b.jpeg "(2+3i)(2-3i) State The Value Of A And B")
Multiplying Complex Numbers: (2 + 3i)(2 - 3i)
This problem involves multiplying two complex numbers. Let's break it down step-by-step:
Understanding Complex Numbers
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1 (i.e., i² = -1).
Multiplying Complex Numbers
We can multiply complex numbers using the distributive property (FOIL method):
(2 + 3i)(2 - 3i) = 2(2) + 2(-3i) + 3i(2) + 3i(-3i)
Simplifying the multiplication:
= 4 - 6i + 6i - 9i²
Since i² = -1:
= 4 - 9(-1)
= 4 + 9
= 13
Result and Values of a and b
The product of (2 + 3i)(2 - 3i) is 13. We can express this result in the standard complex number form (a + bi):
13 = 13 + 0i
Therefore, a = 13 and b = 0.