Math Problem Statement

Can you help simplify this expression? (3 + 2i) - (1 - 4i)?

Solution

Certainly! Let's simplify the expression step by step:

(3+2i)(14i)(3 + 2i) - (1 - 4i)

First, distribute the minus sign across the second parentheses:

3+2i1+4i3 + 2i - 1 + 4i

Now, group the real and imaginary terms together:

(31)+(2i+4i)(3 - 1) + (2i + 4i)

Simplifying both:

2+6i2 + 6i

So, the simplified expression is:

2+6i2 + 6i

Would you like any further explanation or have any more questions?

Related Questions:

  1. How do you add or subtract complex numbers?
  2. How do you multiply complex numbers?
  3. What is the conjugate of a complex number, and how is it used?
  4. Can you express complex numbers in polar form?
  5. How do you divide complex numbers?

Tip:

When simplifying expressions with complex numbers, always separate real and imaginary parts to keep things clear!

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Algebra

Formulas

a + bi - (c + di) = (a - c) + (b + d)i

Theorems

Addition and subtraction of complex numbers

Suitable Grade Level

Grades 9-11