Final answer:
The expression (5-4i)(3+6i) multiplies out to 39 + 18i when using the distributive property and simplifying.
This is the expression in standard form for a complex number with a real part of 39 and an imaginary part of 18i.
Step-by-step explanation:
The expression (5-4i)(3+6i) can be written as a complex number in standard form by using the distributive property, also known as the FOIL method for binomials.
To do this, you multiply each term in the first complex number by each term in the second complex number.
Multiplying each term:
- (5)(3) = 15
- (5)(6i) = 30i
- (-4i)(3) = -12i
- (-4i)(6i) = -24i^2
Since i^2 = -1, we can substitute -1 for i^2 in -24i^2 to get +24.
Now, combine like terms to get the complex number in standard form:
- Real parts: 15 + 24 = 39
- Imaginary parts: 30i - 12i = 18i
Therefore, (5-4i)(3+6i) = 39 + 18i in standard form.