Complex Numbers Math Example 2

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Example 2

medium
Multiply (3+2i)(1−i)(3 + 2i)(1 - i) and write the result in standard form a+bia + bi.

Solution

  1. 1
    Expand using FOIL: (3)(1)+(3)(−i)+(2i)(1)+(2i)(−i)(3)(1) + (3)(-i) + (2i)(1) + (2i)(-i).
  2. 2
    Simplify each term: 3−3i+2i−2i23 - 3i + 2i - 2i^2.
  3. 3
    Replace i2=−1i^2 = -1: 3−3i+2i−2(−1)=3−i+2=5−i3 - 3i + 2i - 2(-1) = 3 - i + 2 = 5 - i.

Answer

5−i5 - i
Complex multiplication uses the distributive property (FOIL) just like binomial multiplication. The key step is replacing i2i^2 with −1-1, which converts the imaginary squared term into a real number.

About Complex Numbers

Numbers of the form a+bia + bi where a,ba, b are real and i=−1i = \sqrt{-1}; they extend the real numbers to solve x2=−1x^2 = -1.

Learn more about Complex Numbers →

More Complex Numbers Examples

Example 1 easy

Simplify [formula], [formula], and [formula].

Example 3 easy

Add [formula].

Example 4 medium

Simplify [formula].

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