# Thread: polar expression and argand diagram

1. ## polar expression and argand diagram

hello guys. am kind of new to the polar topic and have limited resources where notes and text book is concerned.

given that $\displaystyle z_1 = 4 + 3i$ and $\displaystyle z_2= 3-2i$

a) express $\displaystyle z3= z_1 . z_2$ in polar form

for that i have$\displaystyle (4+3i)(2-2i)$
= $\displaystyle 8-8i+6i+6i^2$
=$\displaystyle 8-2i -6$
=$\displaystyle 2+14i$
is this correct?

can someone please show me how to evaluate
$\displaystyle \mid z_1\mid$

$\displaystyle \mid z_2\mid$

$\displaystyle \mid z_3\mid$

and how would i sketch on same argand diagram?

2. ## Complex numbers

Hi

z1.z2=(4+3i)(3-2i)

=12-8i+9i-6i^2
=12+i+6
=18+i.

To graph this on an Argand Diagram think of x axis = real numbers eg. 18 and y axis =imaginary or i axis. Line starts from the origin and extends to coordinates (Re,i)=(18,1)=z3=z1.z2

3. Originally Posted by Neverquit
Hi

z1.z2=(4+3i)(3-2i)

=12-8i+9i-6i^2
=12+i+6
=18+i.

To graph this on an Argand Diagram think of x axis = real numbers eg. 18 and y axis =imaginary or i axis. Line starts from the origin and extends to coordinates (Re,i)=(18,1)=z3=z1.z2
thanks for that correction. but how would i evaluate the modulus the elements..

4. ## modulus

Modulus of a complex number

The modulus r of a complex number z = a + ib is written | z | and defined by | z | =

I hope that helps!