What happens if you multiply a complex number by i?

Multiplying a complex number by i. The point z in C is located x units to the right of the imaginary axis and y units above the real axis. The point z i is located y units to the left, and x units above. Then we can say that multiplication by –i gives a –90° rotation about 0, or if you prefer, a 270° rotation about 0.

What happens when you multiply a number by 1?

The Rule. If you noticed, when you multiply by 1, you always get your original number. This rule tells us that anything multiplied by 1 is itself. We can use this rule on any multiplication by 1 problem.

What does multiply by a form of 1 mean?

If we multiply it by 1, we won’t change its value. If we multiply it by anything equivalent to 1 (such as ), we also won’t change its value. Since each of our two mini-fractions has a 3 in its denominator, what happens if we multiply the whole thing by? Our new numerator is , and our new denominator is .

What is the complex conjugate of 1?

The conjugate of a complex number a + bi (with real coefficients a, b) is what you get when you “replace” i with -i, namely a – bi. For example, the conjugate of i is -i, the “other” square root of -1.

What happens when you multiply a complex number by its conjugate?

The complex conjugate has a very special property. Consider what happens when we multiply a complex number by its complex conjugate. We find that the answer is a purely real number – it has no imaginary part. This always happens when a complex number is multiplied by its conjugate – the result is real number.

What is the sum when we add a number by 1?

When 1 is added to a number, the sum equals the successor of the number.

What happens when you multiply a positive number by a positive number less than 1?

Whenever you multiply a positive number by a positive factor less than 1, the product will be smaller than the original number. For example, \frac 12 \times\frac 34 = \frac 38. Both factors are less than 1, and the product is less than both factors.

How do you multiply complex numbers in rectangular form?

To add complex numbers in rectangular form, add the real components and add the imaginary components. Subtraction is similar. To multiply complex numbers in polar form, multiply the magnitudes and add the angles.