Complex Numbers (1 Viewer)

[ashokkumar]

Can someone please show me how to do the following question:


State the modulus and argument of -1 + i. Hence write (-1 + i)^18 in the form a + ib

Answer: -512i


(For some reason, i always get a very very small real part of my complex number along with -512i.)

 

[ninetypercent]

mod - 1 + i = root 2
arg - 1 + i = 3pi/4

- 1 + i = root 2 cis 3pi/4

(-1 + i)^ 18 = (root2)^18 cis 3pi/4 x 18
= 512 cis -(pi/2)
= 512(-i)
= - 512i

 

[ilikebeeef]

Can someone please show me how to do the following question:


State the modulus and argument of -1 + i. Hence write (-1 + i)^18 in the form a + ib

Answer: -512i


(For some reason, i always get a very very small real part of my complex number along with -512i.)

Modulus = square root 2
Argument = 135 degrees

(-1+i)^18
= (sqrt2cis135)^18
= 512cis2430
= 512cis270
= 512cis(-90)
= -512i

 

[Cazic]

-1 + i is in the second quadrant, so use:



Now,



Finally,

 

[ilikebeeef]

-1 + i is in the second quadrant, so use:



Now,



The excess working out is unnecessary for this situation because it's pretty obvious upon looking at 1+i what the modulus and argument are.

 

[Cazic]

They were getting the wrong answer, which was presumably because they messed up their modulus and/or argument, so I showed how to find them, or they messed up their simplification of their argument, so I explicitly showed the simplified argument.

In general though, allow me to quote many a great maths teacher: "Show your working!" Seriously, it's just how you learn maths.

 

[ilikebeeef]

They were getting the wrong answer, which was presumably because they messed up their modulus and/or argument, so I showed how to find them, or they messed up their simplification of their argument, so I explicitly showed the simplified argument.

For 1+i you can just draw it on an Argand diagram in your mind (or on paper if you're struggling with that) then you can tell the argument (from just looking at the graph) and the modulus (by using mental Pythagora's Theorem).

In general though, allow me to quote many a great maths teacher: "Show your working!" Seriously, it's just how you learn maths.

Yes but in this case it's too obvious lol. Sometimes esp in exams, you need to be time-efficient.

 

[Cazic]

Fair enough.