ok i have to divide complex numbers:
question is: 1-2i+i^3/1+i
this is what i did:
1-2i+i(-i)/1+i
1-2i-i^2/1+i
1-2i-i(-1)/1+i
1-2i+i/1+i
1-3i/1+i*1-i/1-i
1-i-3i+3i^2/1-i+i-i^2
1-i-3i+3(-1)/1-i^2
1-i-3i-3/1-(-1)
1-4i-3/2
-2-4i/2
my answer is -2i-1
is that right?
Be more specific with parentheses. Does the 1+i divide into only the i^3 term? Or does it divide into 1 - 2i + i^3?
from what you showed in your work I will asssume you meant
(1-2i+i^3)/(1+i)
you messed up in your first line.
remember i^3 = i(i^2) = i(-1) = -i
so
(1-2i+i^3)/(1+i)
= (1-2i - i)/1+i)
= (1-3i)/(1+i)
now multiply top and bottom by 1-i to get
(1-4i - 3i^2)/(1 - i^2)
= (4-4i)/2
= 2 - 2i
To divide complex numbers, you can use the following steps:
Step 1: Rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
In this case, the conjugate of 1+i is 1-i. Therefore, multiply both the numerator and denominator by 1-i:
(1-2i+i^3) * (1-i) / (1+i) * (1-i)
Step 2: Simplify the terms in the numerator and denominator.
In the numerator:
- Multiply (1-2i+i^3) and (1-i):
(1-2i+i^3)(1-i) = 1 - i - 2i + 2i^2 + i^3 - i^4
= 1 - 3i - 2 + 2(-1) + (-i)
= -1 - 4i + 2i - i
= -1 - 3i
In the denominator:
- Multiply (1+i) and (1-i):
(1+i)(1-i) = 1 - i + i - i^2
= 1 - i + i + 1
= 2
Step 3: Divide the terms in the numerator by the denominator.
(-1 - 3i) / 2
So, the answer to the division of the complex numbers is (-1 - 3i) / 2.
Your answer of -2i - 1 is incorrect.