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lrp3395
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I don't really understand how to multiply and divide when numbers are in a+bi form
lrp3395 said:I don't really understand how to multiply and divide when numbers are in a+bi form
lrp3395 said:I don't really understand how to multiply and divide when numbers are in a+bi form
Imaginary numbers are numbers that can be written in the form of a+bi, where a and b are real numbers and i is the imaginary unit (defined as the square root of -1).
To multiply imaginary numbers, you can use the FOIL method, just like with regular numbers. For example, (2+3i) * (4+5i) would be equal to 8+10i+12i+15i^2. Simplifying this, we get 8+22i-15, which equals -7+22i.
Imaginary numbers are used to solve mathematical problems that involve negative numbers, such as taking the square root of a negative number. They also have many applications in fields such as engineering, physics, and electronics.
Yes, you can divide imaginary numbers. To divide by a complex number, multiply the numerator and denominator by the complex conjugate of the denominator. For example, (5+2i) / (3-4i) becomes [(5+2i) * (3+4i)] / [(3-4i) * (3+4i)], which simplifies to (23+26i) / 25.
The main difference is that when multiplying imaginary numbers, you add the exponents of i, while when dividing, you subtract the exponents of i. For example, (2i)^3 would be equal to 8i^3, which can be simplified to -8i. On the other hand, (2i)^-3 would be equal to 1 / (8i^3), which simplifies to -1 / 8i.