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How do you convert a complex number from polar form into rectangular form?
Wiki User
∙ 14y ago
If the polar coordinates of a complex number are (r,a) where r is the distance from the origin and a the angle made with the x axis, then the cartesian coordinates of the point are:
x = r*cos(a) and
y = r*sin(a)
Wiki User
∙ 14y ago
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How do change a complex number to its standard form?
It isn't clear in what form you have the complex number. But you can change it from the form (absolute value, angle) to the form (real part + imaginary part) using the polar-rectangular conversion available on scientific calculators (and the other way round, with the rectangular-polar conversion). Note that a complex number in the form (real part + imaginary part) is most appropriate for addition and subtraction, while a complex number of the form (absolute value, angle) is most appropriate for multiplication or division, so depending on the operations, you may want to convert back and forth several times.
What is the exponential form for complex numbers?
Exponential form is similar to 'polar form'. Call the Magnitude A, and the angle θ .Then the number is represented as A*eiθ (θ in radians). To convert to rectangular form, use Euler's formula:eiθ = cos(θ) + i*sin(θ)So the complex number A*eiθ = A*cos(θ) + A*i*sin(θ)
How do you convert the complex number minus i into polar form?
A COMPLEX NUMBER CAN BE CONVERTED INTO A POLAR FORM LET US TAKE COMPLEX NUMBER BE Z=a+ib a is the real number and b is the imaginary number THEN MOD OF Z IS SQUARE ROOT OF a2+b2 MOD OF Z CAN ALSO BE REPRESENTED BY r . THEN THE MOD AMPLITUDE FORM IS r(cos@Very interesting, but -i is not a complex no. it is a simple (imaginary) no. with no real part.
How do you convert the complex number 4 to polar form?
This doesn't need much conversion. Since the coefficient of i is zero the number is on the real axis. Since it has zero angle with the axis, the polar co-ordinates stare you in the face : r is 4, theta is 0.
How do you convret polar form of complex number into algebraic form?
For a complex number in polar form with Magnitude, and Angle: (Magnitude)*(cos(angle) + i*sin(angle)) will give the form: a + bi
Convert the following complex number into its polar representation: 2 + 2i?
2sqrt2(cos45 + i * sin45)
How do change a complex number to its standard form?
It isn't clear in what form you have the complex number. But you can change it from the form (absolute value, angle) to the form (real part + imaginary part) using the polar-rectangular conversion available on scientific calculators (and the other way round, with the rectangular-polar conversion). Note that a complex number in the form (real part + imaginary part) is most appropriate for addition and subtraction, while a complex number of the form (absolute value, angle) is most appropriate for multiplication or division, so depending on the operations, you may want to convert back and forth several times.
How do you convert polar to rectangular coordinates?
If the polar coordinates of a point P are (r,a) then the rectangular coordinates of P are x = rcos(a) and y = rsin(a).
What is the exponential form for complex numbers?
Exponential form is similar to 'polar form'. Call the Magnitude A, and the angle θ .Then the number is represented as A*eiθ (θ in radians). To convert to rectangular form, use Euler's formula:eiθ = cos(θ) + i*sin(θ)So the complex number A*eiθ = A*cos(θ) + A*i*sin(θ)
Why can't we add and subtract polar form of complex numbers and multiply and divide the rectangular form of complex number?
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.)
How do you convert the complex number minus i into polar form?
A COMPLEX NUMBER CAN BE CONVERTED INTO A POLAR FORM LET US TAKE COMPLEX NUMBER BE Z=a+ib a is the real number and b is the imaginary number THEN MOD OF Z IS SQUARE ROOT OF a2+b2 MOD OF Z CAN ALSO BE REPRESENTED BY r . THEN THE MOD AMPLITUDE FORM IS r(cos@Very interesting, but -i is not a complex no. it is a simple (imaginary) no. with no real part.
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.
How do you convert the complex number 4 to polar form?
This doesn't need much conversion. Since the coefficient of i is zero the number is on the real axis. Since it has zero angle with the axis, the polar co-ordinates stare you in the face : r is 4, theta is 0.
Find the resultant of 150N and 200N acting at an angle of 30?
Here is how to solve this. Decide on a direction for each vector. Use your scientific calculator to do a polar-to-rectangular conversion - i.e., separate each vector in horizontal and vertical components. (Check your calculator's manual on how to carry out a polar-to-rectangular conversion.) Add the vectors by components. Finally, convert back to polar (rectangular-to-polar conversion, on your scientific calculator).
How do you convret polar form of complex number into algebraic form?
For a complex number in polar form with Magnitude, and Angle: (Magnitude)*(cos(angle) + i*sin(angle)) will give the form: a + bi
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.
How complex quantity can be expressed?
Complex quantities are points on a coordinate system; the horizontal axis is called the real numbers, the vertical axis, the imaginary numbers.The point that represents a complex number can be expressed:a) In rectangular coordinates, by specifying both coordinates, for example, 5 + 3ib) In polar coordinates, you specify a distance from the origin, and an angle, for example, 10 (angle symbol) 30 degrees.It turns out that addition and subtraction are easier with rectangular coordinates, whereas multiplication, division, and therefore also powers and roots, are easier with polar coordinates.Complex quantities are points on a coordinate system; the horizontal axis is called the real numbers, the vertical axis, the imaginary numbers.The point that represents a complex number can be expressed:a) In rectangular coordinates, by specifying both coordinates, for example, 5 + 3ib) In polar coordinates, you specify a distance from the origin, and an angle, for example, 10 (angle symbol) 30 degrees.It turns out that addition and subtraction are easier with rectangular coordinates, whereas multiplication, division, and therefore also powers and roots, are easier with polar coordinates.Complex quantities are points on a coordinate system; the horizontal axis is called the real numbers, the vertical axis, the imaginary numbers.The point that represents a complex number can be expressed:a) In rectangular coordinates, by specifying both coordinates, for example, 5 + 3ib) In polar coordinates, you specify a distance from the origin, and an angle, for example, 10 (angle symbol) 30 degrees.It turns out that addition and subtraction are easier with rectangular coordinates, whereas multiplication, division, and therefore also powers and roots, are easier with polar coordinates.Complex quantities are points on a coordinate system; the horizontal axis is called the real numbers, the vertical axis, the imaginary numbers.The point that represents a complex number can be expressed:a) In rectangular coordinates, by specifying both coordinates, for example, 5 + 3ib) In polar coordinates, you specify a distance from the origin, and an angle, for example, 10 (angle symbol) 30 degrees.It turns out that addition and subtraction are easier with rectangular coordinates, whereas multiplication, division, and therefore also powers and roots, are easier with polar coordinates.
