0
Add your answer:
Earn +20 pts
Can the product of two non real complex numbers be a real number?
Yes. Consider as the simplest example: i * i = -1. But there are others: (a + bi)(a - bi) = a² + b². When you multiply conjugates, the result is always real. This is useful when dividing to get a pure real number in the denominator.
Which arithmetic operation requires the use of complex conjugate?
It can be used as a convenient shortcut to calculate the absolute value of the square of a complex number. Just multiply the number by its complex conjugate.I believe it has other uses as well.
How do you rationalizing the denominator?
Generally, the process involves multiplying the numerator and denominator of the fraction by the same number. This number is selected so that the original denominator becomes rational. In the process the numerator may become rational. If the original denominator is of the form √b then you multiply the numerator and denominator by √b/√b. If the original denominator is of the form a+√b then you multiply the numerator and denominator by (a-√b)/(a-√b). NOTE change of sign. There is a similar process, using complex conjugates, if the denominator is a complex number.
Is the sum of two conjugate complex number a real number?
Not necessarily. It can be wholly imaginary.For example, 1 + i actually has two complex conjugates. Most schools will teach you that the complex conjugate is 1 - i. However, -1 + i is also a conjugate for 1 + i. (Their product is -1 times the product of the "normal" conjugate pair).The sum of 1 + i and -1 + i = 2i
DO You always get an irrational number when you multiply a rational number and an irrational number?
Yes.
Can the product of two non real complex numbers be a real number?
Yes. Consider as the simplest example: i * i = -1. But there are others: (a + bi)(a - bi) = a² + b². When you multiply conjugates, the result is always real. This is useful when dividing to get a pure real number in the denominator.
Name 2 complex number that when multiplied together become a real number?
Any pair of complex conjugates do that.
Which arithmetic operation requires the use of complex conjugate?
It can be used as a convenient shortcut to calculate the absolute value of the square of a complex number. Just multiply the number by its complex conjugate.I believe it has other uses as well.
Can you figure out two complex numbers that when mulitplied together become a real number?
3 and 5 are both complex numbers, and if you multiply them together, you get 15, which is a real number. If you were looking for two non-real complex numbers, then any pair of complex conjugates will work. For example, 5+2i times 5-2i is 29.
How many roots in a radical problem if the index is odd?
An odd number. In the complex field, the number of roots is the same as the index. Complex (non-real) roots come in pairs (complex conjugates) so the number of real roots will also be odd.
How do you rationalizing the denominator?
Generally, the process involves multiplying the numerator and denominator of the fraction by the same number. This number is selected so that the original denominator becomes rational. In the process the numerator may become rational. If the original denominator is of the form √b then you multiply the numerator and denominator by √b/√b. If the original denominator is of the form a+√b then you multiply the numerator and denominator by (a-√b)/(a-√b). NOTE change of sign. There is a similar process, using complex conjugates, if the denominator is a complex number.
What is the complex conjugate complex number 8 6i?
Oh, dude, the complex conjugate of 8 + 6i is just flipping the sign of the imaginary part, so it's 8 - 6i. It's like changing your mood from happy to grumpy, but in the world of math. So yeah, that's the deal with complex conjugates.
When the product of two irrational or imaginary numbers equals a rational number then the two factors are called?
They are called conjugates.
What do you get when you multiply a positive by a negative number?
When you multiply a positive number by a negative number you always get a negative number.
Is quadratic formula can be used in complex number?
Yes, if you have an equation az^2 + bz + c = 0 where a, b, and c are complex numbers, you can use the quadratic formula to find the (usually two) possible complex values for z. However, they will usually not be conjugates of each other.
When you times by 5 the answer is always even?
if you multiply an even number by 5 then it will always end in 0 but if you multiply an odd number by 5 then it will always end in 5.
Is the sum of two conjugate complex number a real number?
Not necessarily. It can be wholly imaginary.For example, 1 + i actually has two complex conjugates. Most schools will teach you that the complex conjugate is 1 - i. However, -1 + i is also a conjugate for 1 + i. (Their product is -1 times the product of the "normal" conjugate pair).The sum of 1 + i and -1 + i = 2i
