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Why can't we add and subtract polar form of complex numbers and multiply and divide the rectangular form of complex number?
Wiki User
∙ 13y ago
You can certainly multiply and divide with the rectangular form, but it is somewhat easier in polar form. This is especially relevant if you want to extend to more complicated operations, such as higher powers or taking roots.
As for the polar form, any method to add and subtract them directly would probably be quite complicated, and directly or indirectly involve many of the same calculations that are done in converting from polar to rectangular, and back. Try it! (That is, try to deduce the formulas for adding two complex numbers in polar form.)
Wiki User
∙ 13y ago
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Why you need more than one coordinate system?
That is because - for example - some calculations are easier in polar coordinates, and some are easier in rectangular coordinates. For example, complex numbers are easier to add and subtract in rectangular coordinates, and easier to multiply and divide in polar coordinates.
What two numbers multiply to get -144 but subtract to -7?
-137
What two numbers multiply to -10000 and subtract to 15?
-10015
How to calculate the division of complex number?
for two numbers: a + bi and c + di in rectangular format: (a + bi)/(c + di) can be calculated as follows: Multiply numerator and denominator by complex conjugate of the denominator: ( c - di). This gives (ac - bd + bci - bdi) / (c2 + d2). Now the denominator is a real number. If you have them in polar form: Magnitude<Angle. Then divide the magnitudes and subtract the angles.
What combination of numbers always results in an odd number?
Multiply two odd numbers Add an even and an odd Subtract an odd and an even
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.
Why you need more than one coordinate system?
That is because - for example - some calculations are easier in polar coordinates, and some are easier in rectangular coordinates. For example, complex numbers are easier to add and subtract in rectangular coordinates, and easier to multiply and divide in polar coordinates.
What two numbers multiply to get -144 but subtract to -7?
-137
What two numbers multiply to -10000 and subtract to 15?
-10015
How do you multiply consecutive numbers?
you divide and divide again then multiply then add then subtract then finally get the root
How to calculate the division of complex number?
for two numbers: a + bi and c + di in rectangular format: (a + bi)/(c + di) can be calculated as follows: Multiply numerator and denominator by complex conjugate of the denominator: ( c - di). This gives (ac - bd + bci - bdi) / (c2 + d2). Now the denominator is a real number. If you have them in polar form: Magnitude<Angle. Then divide the magnitudes and subtract the angles.
What combination of numbers always results in an odd number?
Multiply two odd numbers Add an even and an odd Subtract an odd and an even
What are the 4 fundamental operations on whole numbers?
add, subtract, multiply, divide
What are the four fundamentals operation with decimal numbers?
Add, subtract, multiply and divide.
What two numbers multiply to give you 70 and subtract to give you 1?
69
What two numbers multiply to get 42 but subtract to get 1?
41
What happens when you add subtract multiply and divide rational numbers?
If you add, subtract or multiply rational numbers, the result will be a rational number. It will also be so if you divide by a non-zero rational number. But division by zero is not defined.
