Studdy AI Logo
Math  /  Algebra

Question32) (2−4i)(−2−4i)(2-4 i)(-2-4 i)

Studdy Solution

STEP 1

1. We are asked to find the product of two complex numbers.
2. The expression involves complex numbers in the form a+bi a + bi .
3. The multiplication of complex numbers follows the distributive property, similar to binomials.

STEP 2

1. Apply the distributive property to multiply the complex numbers.
2. Simplify the expression by combining like terms.
3. Use the property i2=−1 i^2 = -1 to simplify further.

STEP 3

Apply the distributive property (also known as the FOIL method for binomials) to multiply the complex numbers (2−4i)(2-4i) and (−2−4i)(-2-4i):
(2−4i)(−2−4i)=2⋅(−2)+2⋅(−4i)+(−4i)⋅(−2)+(−4i)⋅(−4i)(2-4i)(-2-4i) = 2 \cdot (-2) + 2 \cdot (-4i) + (-4i) \cdot (-2) + (-4i) \cdot (-4i)

STEP 4

Calculate each term:
2⋅(−2)=−42 \cdot (-2) = -4 2⋅(−4i)=−8i2 \cdot (-4i) = -8i (−4i)⋅(−2)=8i(-4i) \cdot (-2) = 8i (−4i)⋅(−4i)=16i2(-4i) \cdot (-4i) = 16i^2

STEP 5

Combine the terms:
−4−8i+8i+16i2-4 - 8i + 8i + 16i^2
Notice that −8i+8i=0-8i + 8i = 0, so the expression simplifies to:
−4+16i2-4 + 16i^2

STEP 6

Use the property i2=−1i^2 = -1 to simplify further:
16i2=16(−1)=−1616i^2 = 16(-1) = -16
Substitute back into the expression:
−4−16=−20-4 - 16 = -20
The equivalent value of the expression is:
−20\boxed{-20}

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