OPERATIONS WITH COMPLEX NUMBERS
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)
Conjugate of complex numbers ?
Let z = 2 + 3i
To find conjugate of any complex number, we have to change sign of imaginary number.
z̄ = 2 - 3i
Dividing complex numbers :
To divide a complex number by another complex number, we have to multiply by the conjugate of the denominator.
Evaluate the expression and write your answer in the form a + bi.
Problem 1 :
(5 - 6i) + (3 + 2i)
Solution:
= (5 - 6i) + (3 + 2i)
= 5 - 6i + 3 + 2i
= 8 - 4i
Problem 2 :
Solution:
Problem 3 :
(2 + 5i)(4 - i)
Solution:
= (2 + 5i)(4 - i)
= 8 - 2i + 20i - 5i2
= 8 + 18i + 5
= 13 + 18i
Problem 4 :
(1 - 2i)(8 - 3i)
Solution:
= (1 - 2i)(8 - 3i)
= 8 - 3i - 16i + 6i2
= 8 - 19i - 6
= 2 - 19i
Problem 5 :
Solution:
Problem 6 :
Solution:
Problem 7 :
Solution:
Problem 8 :
Solution:
Problem 9 :
Solution:
Problem 10 :
Solution:
Problem 11 :
i3
Solution:
= i3
= i2 × i
= -1 × i
= -i
Problem 12 :
i100
Solution:
= i100
= (i2)50
= (-1)50
= ((-1)2)25
= 125
= 1
Problem 13 :
√-25
Solution:
Problem 14 :
√-3√-12
Solution:
Recent Articles
-
Finding Range of Values Inequality Problems
May 21, 24 08:51 PM
Finding Range of Values Inequality Problems -
Solving Two Step Inequality Word Problems
May 21, 24 08:51 AM
Solving Two Step Inequality Word Problems -
Exponential Function Context and Data Modeling
May 20, 24 10:45 PM
Exponential Function Context and Data Modeling