Complex number will consists of two parts,
(i) Real part
(ii) Imaginary part
General form of complex number is a + ib
Here a is real and b is imaginary.
How to add complex numbers ?
Consider two complex numbers,
Let z1 = a + ib and z2 = c + id
z1 + z2 = a + ib + c + id
= (a + c) + ib + id
= (a + c) + i(b + d)
Combining the real parts and combining imaginary parts.
How to subtract complex numbers ?
Consider two complex numbers,
Let z1 = a + ib and z2 = c + id
z1 + z2 = a + ib - (c + id)
= (a + c) - ib - id
= (a + c) - i(b + d)
Combining the real parts and combining imaginary parts.
How to multiply complex numbers ?
Consider two complex numbers,
Let z1 = a + ib and z2 = c + id
z1 z2 = (a + ib)(c + id)
= ac + iad + ibc + i2bd
= ac + iad + ibc + (-1)bd
= ac - bd + i(ad + bc)
Simplify :
Problem 1 :
(-3 + 4i) + (-4 + 7i)
Solution :
= (-3 + 4i) + (-4 + 7i)
= (-3 – 4) + 4i + 7i
= -7 + 11i
Problem 2 :
(3 - 6i) + (7 + 3i)
Solution :
= 3 - 6i + 7 + 3i
= (3 + 7) + 3i - 6i
= 10 - 3i
Problem 3 :
(3 + 8i) + (1 - i)
Solution :
= (3 + 1) + (8i – i)
= 4 + 7i
Problem 4 :
(4 - 4i) + (-4 + 6i)
Solution :
= 4 - 4 - 4i + 6i
= 2i
Problem 5 :
-6i + (3i) - (-7 - 8i)
Solution :
= (-6i) + (3i) - (-7 - 8i)
Distributing negative, we get
= (-6i) + (3i) + 7 + 8i
= -6i + 3i + 8i + 7
= 5i + 7
Problem 6 :
(-5 - 3i) - (8 + i)
Solution :
= (-5 - 3i) - (8 + i)
= -5 - 3i - 8 - i
= -5 - 8 - 3i - i
= -13 – 4i
Problem 7 :
(8 - 5i) - (-4 - 3i)
Solution :
= (8 - 5i) - (-4 - 3i)
= 8 - 5i + 4 + 3i
= 12 – 2i
Problem 8 :
-4 + (7i) - (1 - 5i)
Solution :
-4 + (7i) - (1 - 5i) = (-4 – 1) + (7i – (-5i))
= -5 + 12i
Problem 9 :
(-6 – 6i) – (2 – 2i)
Solution :
= (-6 – 6i) – (2 – 2i)
= -6 - 2 - 6i + 2i
= -8 – 4i
Problem 10 :
(-3i) – (-5 + 7i) + i
Solution :
= (-3i) – (-5 + 7i) + i
= -3i + 5 - 7i + i
= -9i + 5
Problem 11 :
(8i) (-6i) (-3i)
Solution :
(8i) (-6i) (-3i)
= -48i2(-3i)
= 144 i2 i
= 144(-1) i
= -144 i
Problem 12 :
(2i) (3i) (-6i)
Solution :
= (2i) (3i) (-6i)
= 6i2 (-6i)
= -36 ⋅ (i2) i
= -36(-1) i
= 36i
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM