Multiply Complex Numbers Calculator

🔢 Multiply Two Complex Numbers with Step-by-Step Solutions

Calculate the product of two complex numbers \( w = a + bi \) and \( z = c + di \). Complete step-by-step explanation shown.
Complex Multiplication Formula

For \( w = a + bi \) and \( z = c + di \):

\[ w \times z = (a + bi)(c + di) = (ac - bd) + (ad + bc)i \]
Example: Multiply \( (2 + 3i)(4 + 5i) \)
Real part: \( 2 \times 4 - 3 \times 5 = 8 - 15 = -7 \)
Imaginary part: \( 2 \times 5 + 3 \times 4 = 10 + 12 = 22 \)
Result: \( -7 + 22i \)

\( w = a + bi \)

\( z = c + di \)

Enter real and imaginary parts as integers, decimals, or fractions (e.g., 2, 3/4, -5/2).
Product \( w \times z \)
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Enter complex numbers and click "Multiply Complex Numbers"
Step-by-step solution will appear here after calculation.

More References and Links

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