Question

*Find the value of (1 - i)⁴​

Answer 1

Answer:

Decompose your complex vector z=(1+i) in two subvectors:

z=1+i=1+i

The first (black) term is the positive unit real vector (this is always 1). Use this black handle for scaling and rotation.

The residual z−1=i (in your case is purely real). In the figure this is the red line.

Now our starting point is (1+i)1 .

To obtain (1+i)2 grab the black handle, scale it to the length of your previous endpoint |1+i|=(√2) and rotate it to that endpoint, with tan−1(11)=45 degrees. Scale the complete triangle, and now the endpoint of the scaled red vector, is the new complex value, being (1+i)2 .

To obtain (1+i)3 , grab the black handle of the initial triangle again, and scale it to have a length of |(1+i)2|=2 , and rotate it now with 90 degrees. Scale the complete triangle, and now the endpoint of the red vector is at (1+i)3 .

...etcetera...

Second example

Let's repeat this for taking the second power of z=2+2i .

First decompose z into the positive unit real vector (1) and the residual:

2+2i=1+(1+2i)

And use the black handle for scaling and rotation:

Answer 2

Answer:

hope this answer is helpful for you my friend..