Studdy AI Logo
Math  /  Algebra

Question(2−3i)(3−i)(2-3 i)(3-i)

Studdy Solution

STEP 1

1. We are multiplying two complex numbers.
2. The expression can be expanded using the distributive property (also known as the FOIL method for binomials).

STEP 2

1. Expand the expression using the distributive property.
2. Simplify the resulting expression by combining like terms.
3. Use the property i2=−1i^2 = -1 to simplify further.

STEP 3

Use the distributive property to expand the expression (2−3i)(3−i)(2-3i)(3-i):
(2−3i)(3−i)=2⋅3+2⋅(−i)+(−3i)⋅3+(−3i)⋅(−i) (2-3i)(3-i) = 2 \cdot 3 + 2 \cdot (-i) + (-3i) \cdot 3 + (-3i) \cdot (-i)
This results in:
=6−2i−9i+3i2 = 6 - 2i - 9i + 3i^2

STEP 4

Combine the like terms:
6−2i−9i+3i2=6−11i+3i2 6 - 2i - 9i + 3i^2 = 6 - 11i + 3i^2

STEP 5

Use the property i2=−1i^2 = -1 to simplify the expression:
3i2=3(−1)=−3 3i^2 = 3(-1) = -3
Substitute back into the expression:
6−11i−3 6 - 11i - 3

STEP 6

Simplify the expression by combining the real parts:
6−3−11i=3−11i 6 - 3 - 11i = 3 - 11i
Thus, the simplified form of the expression is:
3−11i \boxed{3 - 11i}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord