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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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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