2. Section 9.2
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Combine like terms.
Combine like terms.
Recall that i^2=- 1.
To rationalize a quotient with complex numbers, multiply the numerator and the denominator by the complex conjugate of the denominator.
3+2i
1+4i
5+i
-1/2+5/2i
We can simplify the given expression by combining like terms. This involves treating the imaginary unit i like a variable. Let's do it!
a= 2+3i, b= 1-i
Commutative Property of Addition
Add and subtract terms
We will again treat i as though it was a variable and combine like terms. Let's go!
a= 2+3i, b= 1-i
Distribute -1
Commutative Property of Addition
Add and subtract terms
To evaluate the product of 2 complex numbers, multiply them like polynomials. Recall that i^2 = -1.
a= 2+3i, b= 1-i
Distribute (2+3i)
Distribute - i
i^2=- 1
- a(- b)=a* b
Commutative Property of Addition
Add and subtract terms
Let's substitute our values into the given quotient expression.
a/b ⇔ 2+3i/1-i
Recall that the number pairs x+yi and x-yi are complex conjugates. To write the complex conjugate of a complex number, we only change the sign of the imaginary part. Let's do that for the denominator of our given expression now.
Multiply fractions
Distribute (2+3i)
Distribute i
i^2=- 1
a(- b)=- a * b
Add and subtract terms
Write as a sum of fractions
Put minus sign in front of fraction
a* b/c=a/c* b