Class XI

Complex Numbers and 4 Operations

Lesson

In summary, here is how you undertake the four operations with complex numbers. If you would like to go back to where we covered them in more depth click on the links below.

Addition and Subtraction

To add an subtract complex numbers, add/subtract corresponding real and imaginary components.
Follow all the other rules of algebraic convention

Multiplication

To multiply complex numbers, we follow the rules of algebraic conventions as well as remembering that $i\times i=-1$i×i=−1

Division

Division of complex numbers is carried out by multiplying by a fraction constructed using the conjugate of the denominator. This removes the complex component from the denominator.

Worked Examples

QUESTION 1

Evaluate $\left(3+6i\right)+\left(7+3i\right)$(3+6i)+(7+3i).

QUESTION 2

Simplify $-6\left(3-5i\right)$−6(3−5i).

QUESTION 3

Simplify $-2i\left(4-3i\right)^2$−2i(4−3i)2, leaving your answer in terms of $i$i.

QUESTION 4

Find the value of $\frac{4+6i}{1+i}$4+6i1+i.

Outcomes

11.A.CNQE.1

Need for complex numbers, especially √-1, to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system.