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When dividing complex numbers the first step is to multiply the top and bottom by the complex ----- of the denominator?
Wiki User
∙ 12y ago
"conjugate"
That step is called "rationalizing the denominator", although it actually makes
the denominator 'real', but not necessarily 'rational'.
Wiki User
∙ 12y ago
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When dividing complex numbers the first step is to multiply top and bottom by the conjugate of the denominator?
complex
What is the first step when dividing complex numbers?
The first step when dividing complex numbers is to find the conjugate of the denominator, which is the same expression but with the sign of the imaginary part changed. This is done to eliminate the imaginary part in the denominator.
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.
How do you divide complex numbers?
When dividing complex numbers you must:Write the problem in fractional formRationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator.You must remember that a complex number times its conjugate will give a real number.a complex number 2+2i. the conjugate to this is 2-i1. Multiply both together gives a real number.(2+2i)(2-2i) = 4 -4i + 4i + (-4i2) (and as i2 = -1) = 8To divide a complex number by a real number simply divide the real parts by the divisor.(8+4i)/2 = (4+2i)To divide a real number by a complex number.1. make a fraction of the expression 8/(2+2i)2. multiply by 1. express 1 as a fraction of the divisor's conjunction. 8/(2+2i)*(2-2i)/(2-2i)3. multiply numerator by numerator and denominator by denominator.(16-16i)/84. and simplify 2-2i
What are Three ways to compare improper fractions and mixed numbers?
1) You can convert to a proper fraction with a larger numerator (top number) than denominator (bottom number) then multiply to give you the same denominator. or 2) convert to a decimal number by dividing the numerator by the denominator or 3) covert to a percentage by doing the above and then multiply by 100.
When dividing complex numbers the first step is to multiply top and bottom by the conjugate of the denominator?
complex
What is the first step when dividing complex numbers?
The first step when dividing complex numbers is to find the conjugate of the denominator, which is the same expression but with the sign of the imaginary part changed. This is done to eliminate the imaginary part in the denominator.
Why do you multiply by the complex conjugate?
Whenever a complex number (a + bi) is multiplied by it's conjugate (a - bi), the result is a real number: (a + bi)* (a - bi) = a2 - abi + abi - (bi)2 = a2 - b2i2 = a2 - b2(-1) = a2 + b2 This is useful when dividing complex numbers, because the numerator and denominator can both be multiplied by the denominator's conjugate, to give an equivalent fraction with a real-number denominator.
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.
How do you rationalize complex numbers?
you must multiply by the conjagate. which is the denominator with the middle sign changed....(5+6i)...conjagate= (5-6i)....
How do you divide complex numbers?
When dividing complex numbers you must:Write the problem in fractional formRationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator.You must remember that a complex number times its conjugate will give a real number.a complex number 2+2i. the conjugate to this is 2-i1. Multiply both together gives a real number.(2+2i)(2-2i) = 4 -4i + 4i + (-4i2) (and as i2 = -1) = 8To divide a complex number by a real number simply divide the real parts by the divisor.(8+4i)/2 = (4+2i)To divide a real number by a complex number.1. make a fraction of the expression 8/(2+2i)2. multiply by 1. express 1 as a fraction of the divisor's conjunction. 8/(2+2i)*(2-2i)/(2-2i)3. multiply numerator by numerator and denominator by denominator.(16-16i)/84. and simplify 2-2i
What are complex fractions?
They could be fractions in which the numerator or the denominator, or both, are complex numbers.
What are Three ways to compare improper fractions and mixed numbers?
1) You can convert to a proper fraction with a larger numerator (top number) than denominator (bottom number) then multiply to give you the same denominator. or 2) convert to a decimal number by dividing the numerator by the denominator or 3) covert to a percentage by doing the above and then multiply by 100.
How is dividing mixed numbers the same as dividing fractions?
A mixed number can be converted into an improper fraction. Mixed numbers as improper fractions can be divided just like any other fraction. To convert a mixed number to an improper fraction multiply the whole number by the denominator and add the original numerator to give the new numerator and put this over the original denominator.
How do you convert mix numbers?
multiply the denominator by the whole number, then add the numerator, the denominator is the same as the mixed numbers denominator
How do you write mixed numbers as an inproper fraction?
Multiply the denominator by the whole number, then multiply that by the numerator. Put that answer over the original denominator.
How do you calculate imaginary numbers?
Usually you don't use pure imaginary numbers, but complex numbers - numbers that have a real and an imaginary part. To add and subtract complex numbers, you add and subtract the components (just like any other vector). That is, you add (or subtract) the real part and the imaginary part separately. To multiply them, you multiply the components, just like you would multiply any two polynomials - multiply each part of the first number by each part of the second number. Remember that i2 = -1. Combine the real and the imaginary parts. To divide, consider the division as a fraction, and multiply top and bottom by the complex conjugate. For example, if you are dividing by (2 + 3i), multiply numerator and denominator by (2 - 3i). This will convert the denominator into a real number. Another way to multiply is to convert the complex numbers into polar coordinates (absolute value, i.e., length, and angle). Multiply the absolute values (which are real numbers) together, and simply add the angles. For example, (3 angle 30°) x (4 angle 20°) = (12 angle 50°). You may need to convert the result back to rectangular coordinates in the end. Note that scientific calculators usually have an option to quickly convert from rectangular to polar, or polar to rectangular, coordinates.
