## Complex Numbers operations

Discussions for the Core part of the syllabus. Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths HL Revision Notes

### Complex Numbers operations

Complex Numbers, Operations with complex numbers - IB Mathematics HL

How can we find $z+2w \ ,\ z\cdot w \ ,\ z^2$

given that
$z=3+2i$ and $w=5-2i$

Thanks
lora

Posts: 0
Joined: Wed Apr 10, 2013 7:36 pm

### Re: Complex Numbers operations

The sum (or the difference) of two complex numbers is the complex number which its real part is made up of the sum (or the difference) of their real parts and its imaginary parts is made up of the sum (or the difference) of their imaginary parts.

$z \pm w=(a+bi) \pm (c+id)=(a \pm c)+(b \pm d)i$

Therefore

$z+w=(3+2i)+(5-2i)=(3+5)+(2-2)i=8+0i=8$

The multiplication is performed as usual and using the fact that $i^2=-1$ we have the following

$z \cdot w =(3+2i) \cdot (5-2i)=15-6i+10i-4i^2=19+4i$

and

$z^2=(3+2i)^2=3^2+12i+(2i)^2=9+12i-4=5+12i$
lily

Posts: 0
Joined: Mon Jan 28, 2013 8:04 pm

### Re: Complex Numbers operations

Thanks Lily!!
lora

Posts: 0
Joined: Wed Apr 10, 2013 7:36 pm