Complex Numbers

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1)   In the complex number z = x+ iy, x is the real part of z and y is the imaginary part of z. Complex conjugate of x + iy is x – iy.
2)   In a complex number if the real part is zero (x=0) then it is purely imaginary.
3)   In a complex number if the imaginary part is zero (y=0) then it is a real number.
4)   Polar form z = r e = r (cos θ + i sin θ), r is the length and θ is the angle of the vector.
5)   i² = -1, i³ = -i

Addition of complex numbers:
(p + iq) + (r + is) = (p + r) + (q + s)i

Subtraction of complex numbers:
(p + iq) – (r + is) = (p – r) + ( q – s)i

 
Example 1:   Simplify (3i)(4i)
(a)12i        (b) 12        (c) -12        (d) -12i

Answer: c
Explanation: (3i)(4i) = 12i2 = -12


 
Example 2:   Find the conjugate of -3 +6i
 
Answer: - 3 - 6i


 
Example 3: Express in the form of x + iy
(8 + 2i) + (3 - 7i)
 
Answer: (8 + 3) + i (2 – 7) = 11 – 5i
Example 4: Rationalize
Complex Number
 
Answer:
Complex Number



 

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