simplify (1+3i)(1-5i)
Multiply them out using the FOIL rule.
When you get i², replace by -1.
Using FOIL:
F=1
O=-5i
I=3i
L=-15i²=15
Sum like terms:
(1+3i)(1-5i) = 16-2i
To simplify the expression (1 + 3i)(1 - 5i), you can use the distributive property of multiplication.
First, multiply the real terms (1 and 1):
1 × 1 = 1
Next, multiply the terms with the imaginary units (3i and -5i):
3i × -5i = -15i^2
Remember that i^2 is equal to -1, so we can replace i^2 with -1:
-15 × -1 = 15
Finally, combine the real and imaginary terms:
1 + 15 = 16
The simplified expression is 16.
To reach this answer, you multiplied the real terms, then multiplied the imaginary terms, and then combined the results. Remember to substitute i^2 with -1 when simplifying expressions involving imaginary units.