- What is complex numbers
- |
- Algebra Of complex Numbers
- |
- Conjugate of Complex Numbers
- |
- Modulus of complex numbers
- |
- Argand Plane
- |
- Polar Representation of the complex number
- |
- Rotation of Complex Number
- |
- Identities for Complex Numbers
- |
- Eulers formula and De moivre's theorem
- |
- Cube Root of unity

Multiplying by -i is a rotation of 90 degrees clockwise

z=1

If we multiply it by i, it becomes

z=i so that it has rotated by the angle 90 degrees

We had no solution for the problem

x

Eular was the first mathematicain to introduce solution to this problem,he introduced the symbol i

$ i=\sqrt{(-1)}$

So i

So solution to the problem becomes

x=i or -i

He called the symbol i as imaginary unit.

Just like all the other number ,this number was added to our Number vocabulary. This like other numbers is useful in explaining where physical explanation.

It is very useful in the field Electrical and electronics.

i

i

i

i

i

i

This can be generalized as

For any integer k, i

Find the value $(\frac {i}{2})(\frac {-2i}{3}) (\frac {i^3}{4})$ Solution $(\frac {i}{2})(\frac {-2i}{3}) (\frac {i^3}{4})$ $=\frac {-i^5}{12} = \frac {-i){5}$

For all complex numbers z

1)(z

2)(z

3)(z

(iii) (z

(iv) z

Find the non-zero integral Solution for this equation

$|1-i|^x =2^x$

$|1-i|= \sqrt {2} =2^{1/2}$

So

$2^{x/2}=2^x$

2

2

or x=0

So there is no non-zero integral solution for this equation

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