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Multiply Complex Numbers Calculator.

Multiply two complex numbers in rectangular form.

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Set your values

Results update as you type.

02 / ANSWER

First real part

First imaginary part

Second real part

Second imaginary part

Result

real: -5.00000000 · imaginary: 10.00000000 · magnitude: 11.18033989

Use Cases

Academic Practice

Students can verify their manual multiplication of complex numbers in rectangular form, helping to check homework or practice problems.

Example: Multiply (2 + 3i) and (1 - i) to get 5 + i.

Engineering Calculations

Engineers working with AC circuits or signal processing often need to multiply complex impedances or phasors. This calculator provides quick results.

Example: Multiply (4 + 2i) and (3 - 5i) for circuit analysis.

Frequently Asked Questions

How do I multiply complex numbers using this calculator?: Enter the real and imaginary parts of the first complex number in the 'First real part' and 'First imaginary part' fields, and the second complex number in the 'Second real part' and 'Second imaginary part' fields. The calculator will multiply them and show the result in rectangular form (a + bi).
What is rectangular form of a complex number?: Rectangular form is a way to write a complex number as a + bi, where 'a' is the real part and 'b' is the imaginary part. For example, 3 + 4i has real part 3 and imaginary part 4. This calculator works with numbers in this form.
Can I multiply more than two complex numbers?: No, this calculator is designed to multiply exactly two complex numbers. To multiply more, you can multiply the first two, then use the result as the first number and multiply by the next, and so on.

Tips & Common Mistakes

Tips

Ensure you enter the imaginary part without the 'i' symbol. For example, for 3 + 4i, enter 4 in the imaginary field.
If a complex number has no imaginary part, enter 0 in the imaginary field. For example, 5 is entered as real part 5, imaginary part 0.
Double-check the signs of your imaginary parts. A negative imaginary part should be entered as a negative number.
The result will be in rectangular form, so you can easily convert it to polar form if needed using other tools.

Common Mistakes to Avoid

Forgetting to include the imaginary unit 'i' in the result. The calculator outputs the result as a + bi, so remember that the second number is the coefficient of i.
Entering the imaginary part with the 'i' symbol, such as '4i' instead of '4'. This will cause an error.
Confusing the order of the numbers. The multiplication is commutative, so order doesn't matter, but ensure you enter the correct real and imaginary parts for each number.

Last updated: August 13, 2026

Use Cases

Academic Practice

Students can verify their manual multiplication of complex numbers in rectangular form, helping to check homework or practice problems.

Example: Multiply (2 + 3i) and (1 - i) to get 5 + i.

Engineering Calculations

Engineers working with AC circuits or signal processing often need to multiply complex impedances or phasors. This calculator provides quick results.

Example: Multiply (4 + 2i) and (3 - 5i) for circuit analysis.

Frequently Asked Questions

How do I multiply complex numbers using this calculator?

Enter the real and imaginary parts of the first complex number in the 'First real part' and 'First imaginary part' fields, and the second complex number in the 'Second real part' and 'Second imaginary part' fields. The calculator will multiply them and show the result in rectangular form (a + bi).

What is rectangular form of a complex number?

Rectangular form is a way to write a complex number as a + bi, where 'a' is the real part and 'b' is the imaginary part. For example, 3 + 4i has real part 3 and imaginary part 4. This calculator works with numbers in this form.

Can I multiply more than two complex numbers?

No, this calculator is designed to multiply exactly two complex numbers. To multiply more, you can multiply the first two, then use the result as the first number and multiply by the next, and so on.

Tips & Common Mistakes

Tips

Ensure you enter the imaginary part without the 'i' symbol. For example, for 3 + 4i, enter 4 in the imaginary field.
If a complex number has no imaginary part, enter 0 in the imaginary field. For example, 5 is entered as real part 5, imaginary part 0.
Double-check the signs of your imaginary parts. A negative imaginary part should be entered as a negative number.
The result will be in rectangular form, so you can easily convert it to polar form if needed using other tools.

Common Mistakes to Avoid

Forgetting to include the imaginary unit 'i' in the result. The calculator outputs the result as a + bi, so remember that the second number is the coefficient of i.
Entering the imaginary part with the 'i' symbol, such as '4i' instead of '4'. This will cause an error.
Confusing the order of the numbers. The multiplication is commutative, so order doesn't matter, but ensure you enter the correct real and imaginary parts for each number.

Use Cases

Academic Practice

Students can verify their manual multiplication of complex numbers in rectangular form, helping to check homework or practice problems.

Example: Multiply (2 + 3i) and (1 - i) to get 5 + i.

Engineering Calculations

Engineers working with AC circuits or signal processing often need to multiply complex impedances or phasors. This calculator provides quick results.

Example: Multiply (4 + 2i) and (3 - 5i) for circuit analysis.

Frequently Asked Questions

How do I multiply complex numbers using this calculator?

What is rectangular form of a complex number?

Can I multiply more than two complex numbers?

No, this calculator is designed to multiply exactly two complex numbers. To multiply more, you can multiply the first two, then use the result as the first number and multiply by the next, and so on.

Tips & Common Mistakes

Tips

Ensure you enter the imaginary part without the 'i' symbol. For example, for 3 + 4i, enter 4 in the imaginary field.
If a complex number has no imaginary part, enter 0 in the imaginary field. For example, 5 is entered as real part 5, imaginary part 0.
Double-check the signs of your imaginary parts. A negative imaginary part should be entered as a negative number.
The result will be in rectangular form, so you can easily convert it to polar form if needed using other tools.

Common Mistakes to Avoid

Forgetting to include the imaginary unit 'i' in the result. The calculator outputs the result as a + bi, so remember that the second number is the coefficient of i.
Entering the imaginary part with the 'i' symbol, such as '4i' instead of '4'. This will cause an error.
Confusing the order of the numbers. The multiplication is commutative, so order doesn't matter, but ensure you enter the correct real and imaginary parts for each number.