Polar form of complex numbers

Polar form of complex numbers

Knowing the argument and the modulus of a complex number allows us to convert a complex number from its rectangular form, which is what we have been using thus far, to its other basic form – polar form. We will see that while a complex number in rectangular form is denoted by its horizontal and vertical components, a complex number in polar form is denoted by its magnitude and argument.
Basic Concepts: Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}, Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} ), Solving expressions using 45-45-90 special right triangles , Solving expressions using 30-60-90 special right triangles
Related Concepts: Imaginary zeros of polynomials, Magnitude of a vector, Direction angle of a vector

Lessons

  • 1.
    Convert the following complex numbers from rectangular form to polar form
    a)
    z=2i−3 z=2i-3

    b)
    w=−5−3iw=-5-3i

    c)
    z=4−i z=4-i

  • 2.
    Convert the following complex numbers from polar form to rectangular form
    a)
    z=4(cos⁡(π4)+isin⁡(π4)) z=4(\cos(\frac{\pi}{4})+i\sin(\frac{\pi}{4}))

    b)
    w=13(cos⁡(180∘)+isin⁡(180∘)) w=13(\cos(180^{\circ})+i\sin(180^{\circ}))

    c)
    z=4(cos⁡(5π3)+isin⁡(5π3)) z=4(\cos(\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))

  • 3.
    Given that z=4−3iz=4-3i , and w=2−iw=2-i, find z+wz+w and express it in polar form
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19.
Imaginary and Complex Numbers
19.1
Introduction to imaginary numbers
19.2
Complex numbers and complex planes
19.3
Adding and subtracting complex numbers
19.4
Complex conjugates
19.5
Multiplying and dividing complex numbers
19.6
Distance and midpoint of complex numbers
19.7
Angle and absolute value of complex numbers
19.8
Polar form of complex numbers
19.9
Operations on complex numbers in polar form
Grade 12 Math
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