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India
Class XI

Addition and Subtraction of Complex Numbers

Lesson

Complex numbers can be added and subtracted very easily, following the normal laws of algebra. 

We must only add and subtract like terms.

And in complex numbers, like terms are the real parts and the imaginary parts.

 

Let's look a an example with two complex numbers $z_1=3+2i$z1=3+2i and $z_2=6-4i$z2=64i

To add these two complex numbers together we must first identify the real and imaginary components of each. 

 

Then we add the real components, and imaginary components respectfully

 

Here are a few more examples

Example 1
$\left(3+7i\right)+\left(2+i\right)$(3+7i)+(2+i) $=$= $\left(2+3\right)+\left(7+1\right)i$(2+3)+(7+1)i
  $=$= $5+8i$5+8i

See how in this example I grouped the real and imaginary parts and then added.  Sometimes this helps keep track of all the components.  Sometimes you can jump straight to the answer. 

 

Example 2
$\left(9-2i\right)-\left(-2+6i\right)$(92i)(2+6i) $=$= $9-2i+2-6i$92i+26i
  $=$= $11-8i$118i

In this example, I expanded the brackets observing the change of sign and then collected like terms. 

More Worked Examples

QUESTION 1

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

QUESTION 2

Evaluate $\left(6+9i\right)-\left(-3-4i\right)$(6+9i)(34i).

QUESTION 3

Evaluate $\left(-6\sqrt{7}-2i\right)+\left(3\sqrt{7}+7i\right)$(672i)+(37+7i).

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.

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