Multiple each of the following and write the answers in standard form.
1.(1-4i)(-6+3i)
2. (1-3i)(1+3i)
1.(1-4i)(-6+3i)
= -6 + 3i + 24i - 12i^2
= -6 + 27i + 12 , because i^2 = -1
= 6 + 27i
do #2 the same way
treat them like regular binomials, remembering that i^2 = -1
I'll do one, and then you can do any others in the same way.
(1-4i)(-6+3i)
= 1(-6+3i) - 4i(-6+3i)
= -6 + 3i + 24i - 12i^2
= -6 + 27i + 12
= 6 + 27i
You can always go to some site like wolframalpha.com to verify your answers. Just type it in and hit return.
To multiply complex numbers, we can use the foil method, just like multiplying binomials. FOIL stands for First, Outer, Inner, Last.
1. Let's multiply (1 - 4i) and (-6 + 3i):
First, multiply the first terms:
(1) × (-6) = -6
Outer, multiply the terms on the outside:
(1) × (3i) = 3i
Inner, multiply the terms on the inside:
(-4i) × (-6) = 24i
Last, multiply the last terms:
(-4i) × (3i) = -12i^2
Now, we can combine the terms:
-6 + 3i + 24i - 12i^2
Remember that i^2 is defined as -1, so we can simplify further:
-6 + 3i + 24i + 12
Combine like terms:
6 + 27i
So, the answer in standard form is 6 + 27i.
2. Let's multiply (1 - 3i) and (1 + 3i):
First, multiply the first terms:
(1) × (1) = 1
Outer, multiply the terms on the outside:
(1) × (3i) = 3i
Inner, multiply the terms on the inside:
(-3i) × (1) = -3i
Last, multiply the last terms:
(-3i) × (3i) = -9i^2
Similar to the previous example, i^2 is -1:
1 + 3i - 3i -9i^2
Combine like terms:
1 - 9i^2
Again, i^2 is -1:
1 - 9(-1)
Simplify further:
1 + 9
The answer in standard form is 10.