SOLUTION: Hello. My son is struggling with complex numbers and this stuff is like a second language to me. Any help is greatly appreciated. Thanks. 1) 4i^5-6i^4+3i^3-9i^2 2) 3i^4-(2i-6

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Hello. My son is struggling with complex numbers and this stuff is like a second language to me. Any help is greatly appreciated. Thanks. 1) 4i^5-6i^4+3i^3-9i^2 2) 3i^4-(2i-6      Log On


   

Question 394194: Hello. My son is struggling with complex numbers and this stuff is like a second language to me. Any help is greatly appreciated. Thanks.
1) 4i^5-6i^4+3i^3-9i^2
2) 3i^4-(2i-6)-5i^2+(2+12i)
3) (4i-5)*(5i-4)
4) (5i+8)/(3i)
5) (11-3i)/(4+5i)
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Note:
i = i
i^2 = -1
i^3 = -i
i^4 = 1
etc.
-------
1) 4i^5-6i^4+3i^3-9i^2
= 4i - 6*1+3(-i)-9(-1)
---
= -6+9+4i-3i
= 3+i
--------------------------

2) 3i^4-(2i-6)-5i^2+(2+12i)
= 3-2i+6-5(-1)+2+12i
---
= 3+6+4+2 -2i+12i
---
= 15+10i
----------------------------
3) (4i-5)*(5i-4)
= 20i^2-16i-25i+20
= -20+20-41i
= -41i
---------------------------------
4) (5i+8)/(3i)
= [(-3i)(5i+8)]/[(-3i)(3i)]
---
= [15-24i]/9
---
= [5-8i]/3
---------------------------------
5) (11-3i)/(4+5i)
= [(11-3i)(4-5i)]/[(4+5i)(4-5i)]
---
= [44-55i-12i-15]/[16+25]
---
= [29-67i]/41
=================
Cheers,
Stan H.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1.
4i%5E5-6i%5E4%2B3i%5E3-9i%5E2+
.........%28i%5E2%29=-1
4%28-1%29%28-1%29%28i%29+-+6%28-1%29%28-1%29+%2B+3%28-1%29%28i%29+-+9%28-1%29+
4i+-+6+-+3i+%2B+9+
i+%2B+3+

2) 3i%5E4-%282i-6%29-5i%5E2%2B%282%2B12i%29+
3%28i%5E2%29%28i%5E2%29-+2i+%2B+6+-5i%5E2+%2B2+%2B12i

3%28-1%29%28-1%29-+2i+%2B+6+-5%28-1%29+%2B+2+%2B12i
3+-+2i+%2B+6+%2B5+%2B+2+%2B12i
+16+%2B10i+


3. +%284i-5%29%2A%285i-4%29+.....multiply
+%28%284i%29%285i%29+-%284i%29%284%29+-5%285i%29+%2B+5%2A4%29
+%28%2820i%5E2%29+-%2816i%29+-25i+%2B+20%29
+%28%2820%28-1%29%29+-16i+-25i+%2B+20%29
+cross%28-20%29+-16i+-25i+%2Bcross%28+20%29%29
+-16i+-25i%29
+-41i%29

4) %285i%2B8%29%2F%283i%29

%285i%2B8%29%2F%283i%29.........multiply by 3i to eliminate i from denominator

%285i%2B8%29%283i%29%2F%283i%29%283i%29

%285i%2B8%29%283i%29%2F%289i%5E2%29

%2815i%5E2%2B24i%29%2F%289%2A-1%29

%2815%28-1%29%2B24i%29%2F%28-9%29

%28-%2815-24i%29%29%2F-9
%2815-24i%29%2F9


5) %2811-3i%29%2F%284%2B5i%29

%2811-3i%29%2F%284%2B5i%29

%2811-3i%29%284-5i%29+%2F%284%2B5i%29%284-5i%29

%2844+-+55i+-12i+%2B15i%5E2%29%2F%2814+-+20i+%2B+20i+-+25i%5E2%29

%2844+-+67i+%2B15%28-1%29%29%2F%2814+-+25%28-1%29%29

%2844+-+67i+-15%29%2F%2814+%2B25%29

%2829+-+67i+%29%2F39