How we can simplify 5i/(1-i) (2-i) (3-i) and (1-i) ^3?💝
💝
Click Like Or Dislike share your opinion 🙏🙏🙏🙏👇👇👇👇👇
Mathe Solution Here.👇👇
To simplify the expressions (1−i)(2−i)(3−i)5i and (1−i)3, we need to perform some algebraic manipulations. Let's start with the first expression:
Simplifying (1−i)(2−i)(3−i)5i
Multiply the denominators:
We need to multiply (1−i), (2−i), and (3−i) in the denominator. To make this easier, we will first multiply two of them, and then multiply the result by the third one.
(1−i)(2−i)=1⋅2+1⋅(−i)−i⋅2−i⋅(−i)=2−i−2i+i2=2−3i+i2
Since i2=−1:
2−3i+(−1)=1−3i
Now multiply (1−3i) by (3−i):
(1−3i)(3−i)=1⋅3+1⋅(−i)−3i⋅3−3i⋅(−i)=3−i−9i+3i2
Again, using i2=−1:
3−i−9i+3(−1)=3−i−9i−3=−10i
Thus, the denominator is −10i.
Simplify the fraction:
−10i5i=−21
So, (1−i)(2−i)(3−i)5i=−21.
Simplifying (1−i)3
First, find (1−i)2:
(1−i)2=(1−i)(1−i)=1⋅1+1⋅(−i)−i⋅1−i⋅(−i)=1−i−i+i2
Since i2=−1:
1−i−i+(−1)=1−2i−1=−2i
Now, multiply −2i by (1−i):
(1−i)(−2i)=1⋅(−2i)+(−i)⋅(−2i)=−2i+2i2
Again, using i2=−1:
−2i+2(−1)=−2i−2=−2−2i
So, (1−i)3=−2−2i.
Final Results
- (1−i)(2−i)(3−i)5i=−21
- (1−i)3=−2−2i
.jpeg)
.jpeg)