Complex Number Multiplication Quiz

Example 1: (2+3i)(1+2i)

First: Multiply the real parts: 2 × 1 = 2

Outer: Multiply the real part of the first number with the imaginary part of the second number: 2 × 2i = 4i

Inner: Multiply the imaginary part of the first number with the real part of the second number: 3i × 1 = 3i

Last: Multiply the imaginary parts: 3i × 2i = 6i². Remember, i² = -1, so 6i² = -6.

Combining the results: 2 + 4i + 3i – 6 = -4 + 7i

Example 2: (1-i)(2+3i)

First: Multiply the real parts: 1 × 2 = 2

Outer: Multiply the real part of the first number with the imaginary part of the second number: 1 × 3i = 3i

Inner: Multiply the imaginary part of the first number with the real part of the second number: -i × 2 = -2i

Last: Multiply the imaginary parts: -i × 3i = -3i². Remember, i² = -1, so -3i² = 3.

Combining the results: 2 + 3i – 2i + 3 = 5 + i

Example 3: (4-2i)(-1+i)

First: Multiply the real parts: 4 × -1 = -4

Outer: Multiply the real part of the first number with the imaginary part of the second number: 4 × i = 4i

Inner: Multiply the imaginary part of the first number with the real part of the second number: -2i × -1 = 2i

Last: Multiply the imaginary parts: -2i × i = -2i². Remember, i² = -1, so -2i² = 2.

Combining the results: -4 + 4i + 2i + 2 = -2 + 6i