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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^{iθ} = 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

(p + iq) + (r + is) = (p + r) + (q + s)i

(p + iq) – (r + is) = (p – r) + ( q – s)i

(a)12i (b) 12 (c) -12 (d) -12i

**Answer: **c

Explanation: (3i)(4i) = 12i^{2} = -12

(8 + 2i) + (3 - 7i)

Example 4: Rationalize