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By creating a real-imaginary plane (real on horizontal axis, imaginary on vertical), any complex number can be represented graphically. The polar form is a magnitude and angle. The magnitude is measured from the origin to the point on the plane. For a complex number a + bi, this value is a2 + b2. The angle is measured from the positive real axis, clockwise.
For positive imaginary part (b), this will be +arccos(a/(a2 + b2)). (0° to +180°, or 0 to +pi radians)
For negative imaginary part (b), this will be -arccos(a/(a2 + b2)). (0° to -180°, or 0 to -pi radians, or alternatively 180° to 360° or pi to 2pi radians)
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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 mathematician introduced complex numbers?
Gerolamo Cardano is an Italian mathematician who introduced complex numbers. Complex numbers are those that can be expressed in the form of a+bi where a and b represent real numbers.
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 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 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.
