(8-6i)-in-standard-form.jpeg "(7+5i)(8-6i) In Standard Form")
Multiplying Complex Numbers: (7 + 5i)(8 - 6i)
This article will guide you through the process of multiplying complex numbers and expressing the result in standard form (a + bi).
Understanding Complex Numbers
Complex numbers are numbers 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 (i² = -1).
Multiplying Complex Numbers
To multiply complex numbers, we use the distributive property (or FOIL method) just like we would with binomials:
(7 + 5i)(8 - 6i) = 7(8) + 7(-6i) + 5i(8) + 5i(-6i)
Simplifying the Expression
Now, let's simplify the expression:
- 56 - 42i + 40i - 30i²
Remember that i² = -1, so we can substitute:
- 56 - 42i + 40i + 30
Combining Real and Imaginary Terms
Finally, combine the real terms and the imaginary terms:
- (56 + 30) + (-42 + 40)i
Standard Form
The simplified expression in standard form is:
86 - 2i
Therefore, the product of (7 + 5i) and (8 - 6i) expressed in standard form is 86 - 2i.