Multiplying and dividing complex numbers

Multiplying and dividing complex numbers

We will continue to explore other types of operations on complex numbers. This section will focus on performing multiplication and division on complex numbers.
Basic concepts: Exponents: Zero exponent: a0=1 a^0 = 1, Rationalize the denominator , Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2),
Related concepts: Imaginary zeros of polynomials,

Lessons

  • 1.
    Multiplying complex numbers
    a)
    (3+i)×(1+3i)(3+i)\times(1+3i)

    b)
    (1−2i)×(−2+32i) (1-\sqrt{2}i)\times(-2+3\sqrt{2}i)

    c)
    (6−5i)×(6+5i)(6-5i)\times(6+5i)

  • 2.
    Dividing complex numbers
    a)
    (1+2i)÷(3−i) (1+2i)\div(3-i)

    b)
    5−5i−4+5i\frac{5-\sqrt{5}i}{-4+\sqrt{5}i}

    c)
    2−3i3i+2 \frac{2-3i}{3i+2}

  • 3.
    Given that z=5+6i z=5+6i , determine z‾⋅z\overline{z}\cdot z
  • 4.
    Given that w=2−5iw=2-5i , z=3+6iz=3+6i determine w⋅z‾w \cdot \overline{z}
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18.
Imaginary and Complex Numbers
18.1
Introduction to imaginary numbers
18.2
Complex numbers and complex planes
18.3
Adding and subtracting complex numbers
18.4
Complex conjugates
18.5
Multiplying and dividing complex numbers
18.6
Distance and midpoint of complex numbers
18.7
Angle and absolute value of complex numbers
18.8
Polar form of complex numbers
18.9
Operations on complex numbers in polar form
Grade 12 Math
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