Question

What is the trigonometric form of `(2-i)*(3+i)`?

Answer 1

`5sqrt2cis(-8°8')`

Explanation:

Let `z=(2-i)*(3+i)=6+2i-3i-i^2=7+(-1)i`

Modulus:
`|z|=sqrt(7^2+(-1)^2)=sqrt50=5sqrt2`

Argument:
Let `arg(z)=Theta`
`tanTheta=-1/7`
`Theta=-8°8'`

• Be careful when finding the argument, it is always good to plot the complex number on an Argand diagram to determine which quadrant it is in, just so that you write the correct principal argument.

`:.z=5sqrt2(cos(-8°8')+isin(-8°8'))=5sqrt2cis(-8°8')`