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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15.
Complex Numbers and Complex Plane
15.1
Introduction to imaginary numbers
15.2
Complex numbers and complex planes
15.3
Adding and subtracting complex numbers
15.4
Complex conjugates
15.5
Multiplying and dividing complex numbers
15.6
Distance and midpoint of complex numbers
15.7
Angle and absolute value of complex numbers
15.8
Polar form of complex numbers
15.9
Operations on complex numbers in polar form
Precalculus
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