How do I add and multiply complex numbers?
An example of an AI chatbot conversation about complex number operations.
How do I add and multiply complex numbers?
To add complex numbers, combine the real parts and the imaginary parts separately. For example, (2 + 3i) + (4 + 5i) = (2+4) + (3+5)i = 6 + 8i.
What about multiplying them?
To multiply complex numbers, use the distributive property. For example, (2 + 3i) * (4 + 5i) = 8 + 10i + 12i + 15i^2. Remember that i^2 = -1, so it simplifies to -7 + 22i.
Can you give me another example of addition?
Sure! For (1 + 2i) + (3 + 4i), you add the real parts: 1 + 3 = 4, and the imaginary parts: 2 + 4 = 6. So, the result is 4 + 6i.
What if I want to divide complex numbers?
To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator. For example, to divide (2 + 3i) by (4 + 5i), multiply by (4 - 5i) to simplify.
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