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Basically there were more than one form for Complex Numbers. It might be Polar, Trigonometric, Cartesian or Exponential. The important term in Complex Number is also Modulus,|z| or R and Argument, θ.  Below was the example of question and answer for Complex Number.

If we sketch their Argand Diagram then we got

Another one is

For above answer the Argand Diagram is

Usually when the question ask in Trigonometric Form, we should give in Trigonometric Form.  However if your answer in Polar Form or Cartesian Form or Exponential Form still accept except the question was mentioned either answer in Polar, Cartesian or Exponential Form.

Happy Learn Math

I had been received a mathematics question from someone.  Either this is a mathematics problem or just a joke, I had just tried to solve it.  Below was my answer;

- 35

Is it same with your answer ?

The step is:

First: We solve the power

Second: Value in bracket

Third: Divide or Multiply

Finally: Plus or Subtract

How about yours ?

If I do mistake please let me know because I also learn. Thank you

The reciprocal for trigonometric ratio is

cot θ = 1/tan θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

Area of Irregular shape also would be counted by using Simpson’s Rule. Below are formulae for Simpson’s Rule:
h/3(y_0 + 4(y_1,3,5…) + 2(y_2,4,6…) + y_n)

Let’s learn from the basic;
Let say we got a function f(x)=4. the derivative or differentiation for this function is f’(x)=0 or dy/dx = 0. why?
The basic formulae for differentiation when y=ax^n is y’ or dy/dx=anx^(n-1).
Example: find dy/dx for 4x^2
the answer is 4(2)x^(2-1) = 8x

Let say we are given a sequence of number 2, 4, 8, 16, …
Now we can determine either this sequence are geometric progression or not by divide fourth term over third term or second term over first term. Actually this operation is subject to find a common ratio,r.
First term still like arithmetic, we denote as ‘a’. As long as known as a geometric progression, to find n^thterm we use formulae T_n=ar^n-1.
Now, according to last sequence number, let say we want to find the number for fourth term; r=4/2=8/4=2, a=2, T₄=2(2)^4-1=16

A sequence of number which is start with first term, second term, third term and so on till the last term. A different value between first term and second term should be equal with second and third term and so on. Now let’s look at;

Example 1: 3, 5, 7, 9
First term,a is 1, second term is 3…
7-5 = 5-3 (this is the way on how to find what we call a common difference,d. So, the value for common difference is 2.
We use a formula T_n=a+(n-1)d to find n^th term.
Based on previous example, let say we want to know 4^th term. Here we have a=3, d=2, so T₄=3+(4-1)2
T₄=9

Question 1
a) Simplify the following Complex Number
i)i^5+i^20-2i^3
=(i^2)^2•i+(i^2)^10-2(i^2)i
=(-1)^2•i+(-1)^10-2(-1)i
=i+1+2i
=1+3i

ii)3(4+5i)-2(-3-6i)
=(12+15i)-(-6-12i)
=18+27i

Marks Grade
80-100. A
75-79. A-
70-74. B+
65-69. B
60-64. B-
55-59. C+
50-54. C
47-49. D
44-46. D-
40-43. E+
30-39. E
20-29. E-
0-19. F

We use ∫udv = uv – ∫vdu.

Exp. 1: Find ∫x(2x+3)^5 dx

Let u = x , du/dx = 1 , du = dx

dv = (2x=3)^5 dx so v = (2x+3)^6 /12

then use integration by parts:

x(2x=3)^6 /12 – ∫(2x+3)^6/12 dx

x(2x+3)^6 /12 – (2x+3)^7/168 + c

(2x+3)^6/168 [14x - (2x+3)] + c

(2x+3)^6/168 [12x - 3] + c