Math Problem Statement

Find the product and write the result in standard form. −8i(8i−6)

Solution

To find the product of 8i(8i6)-8i(8i - 6), we will apply the distributive property.

8i(8i6)=(8i8i)+(8i6)-8i(8i - 6) = (-8i \cdot 8i) + (-8i \cdot -6)

Now, compute each term:

  1. 8i8i=64i2-8i \cdot 8i = -64i^2
  2. 8i6=48i-8i \cdot -6 = 48i

Next, simplify 64i2-64i^2. Recall that i2=1i^2 = -1, so:

64i2=64(1)=64-64i^2 = -64(-1) = 64

Now, the expression becomes:

64+48i64 + 48i

Thus, the result in standard form is:

64+48i64 + 48i

Would you like any further clarification or details?

Here are 5 related questions to practice:

  1. Simplify 5i(7i+4)5i(7i + 4) and write the result in standard form.
  2. Multiply and simplify: (3i)(4i9)(3i)(4i - 9).
  3. What is the product of 2i(610i)2i(6 - 10i)?
  4. Find the result of 5i(8i+7)-5i(8i + 7) in standard form.
  5. Expand and simplify (2+3i)(4i)(2 + 3i)(4 - i).

Tip: Always remember that i2=1i^2 = -1 when simplifying powers of ii.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Complex Numbers
Distributive Property
Simplification of Imaginary Units

Formulas

Distributive Property: a(b + c) = ab + ac
Imaginary Unit: i^2 = -1

Theorems

Multiplication of Complex Numbers

Suitable Grade Level

Grades 9-12