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- Imaginary and Complex Numbers

Still Confused?

Try reviewing these fundamentals first

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Try reviewing these fundamentals first

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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: $a^0 = 1$, Rationalize the denominator , Find the difference of squares: $(a - b)(a + b) = (a^2 - b^2)$

Related Concepts: Imaginary zeros of polynomials

- 1.Multiplying complex numbersa)$(3+i)\times(1+3i)$b)$(1-\sqrt{2}i)\times(-2+3\sqrt{2}i)$c)$(6-5i)\times(6+5i)$
- 2.Dividing complex numbersa)$(1+2i)\div(3-i)$b)$\frac{5-\sqrt{5}i}{-4+\sqrt{5}i}$c)$\frac{2-3i}{3i+2}$
- 3.Given that $z=5+6i$, determine $\overline{z}\cdot z$
- 4.Given that $w=2-5i$, $z=3+6i$ determine $w \cdot \overline{z}$

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

We have over 860 practice questions in Sixth Year Maths for you to master.

Get Started Now19.1

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