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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.
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How do you convert a complex number from polar form into rectangular form?
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)
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
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)
Convert the following complex number into its polar representation: 2 + 2i?
2sqrt2(cos45 + i * sin45)
How do you convert a complex number from polar form into rectangular form?
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)
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
What is 6 divided by 1 minus i?
5
How do you find square root of a complex number?
This is best done if the complex number is in polar coordinates - that is, a distance from the origin, and an angle. Take the square root of the argument (the absolute value) of the complex number; and half the angle.
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)
A complex number is a number of the form a plus bi where?
"a + bi" is a common way to write a complex number. Here, "a" and "b" are real numbers.Another common way to write a complex number is in polar coordinates - basically specifying the distance from zero, and an angle.
How do you solve a quadratic equation with imaginary numbers?
You just plug in the coefficients, and do the normal operations. Of course you have to know how to calculate with complex numbers. Assuming the coefficients are real, you may at some moment get the root of a negative number. Say, for instance, you have the square root of minus 2, then the solution of that part is the square root of plus 2, multiplied by i.If the original coefficients are complex, you may have to calculate the root of a complex number. This is a little more complicated. For this, you convert the complex number to polar coordinates - that is, to a length and an angle. Then, to actually take the square root, you take half the angle, and the square root of the distance - and convert back to rectangular coordinates (separating the real and the imaginary part). (For the second solution, add 180 degrees to the angle.)
What complex number is a number of the form a plus bi where?
"a + bi" is a common way to write a complex number. Here, "a" and "b" are real numbers.Another common way to write a complex number is in polar coordinates - basically specifying the distance from zero, and an angle.
True or false: When its argument is restricted to (0,2pi), the polar form of a complex number is not unique?
False apex
