To find the operations between z1 and z2, we first need to express them in the standard form a + bi.
Given:z1 = 2 + 8iz2 = 4 - 3i
Now let's perform the operations:
z1 + z2:(2 + 8i) + (4 - 3i)= 2 + 4 + 8i - 3i= 6 + 5i
z1 - z2:(2 + 8i) - (4 - 3i)= 2 - 4 + 8i + 3i= -2 + 11i
z1 / z2:To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator:z1/z2 = (2 + 8i) / (4 - 3i)= (2 + 8i)(4 + 3i) / (4 - 3i)(4 + 3i)= (8 + 6i + 32i - 24) / (16 + 12i - 12i - 9i^2)= (8 + 38i - 24) / (16 + 9)= (16 + 38i) / 25= 0.64 + 1.52i
Next, let's find the square of z1:
Therefore:z1 + z2 = 6 + 5iz1 - z2 = -2 + 11iz1 / z2 = 0.64 + 1.52iz1^2 = -60 + 32i
To find the operations between z1 and z2, we first need to express them in the standard form a + bi.
Given:
z1 = 2 + 8i
z2 = 4 - 3i
Now let's perform the operations:
z1 + z2:
(2 + 8i) + (4 - 3i)
= 2 + 4 + 8i - 3i
= 6 + 5i
z1 - z2:
(2 + 8i) - (4 - 3i)
= 2 - 4 + 8i + 3i
= -2 + 11i
z1 / z2:
To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator:
z1/z2 = (2 + 8i) / (4 - 3i)
= (2 + 8i)(4 + 3i) / (4 - 3i)(4 + 3i)
= (8 + 6i + 32i - 24) / (16 + 12i - 12i - 9i^2)
= (8 + 38i - 24) / (16 + 9)
= (16 + 38i) / 25
= 0.64 + 1.52i
Next, let's find the square of z1:
z1^2:z1^2 = (2 + 8i)^2
= (2 + 8i)(2 + 8i)
= 4 + 16i + 16i + 64i^2
= 4 + 16i + 16i - 64
= -60 + 32i
Therefore:
z1 + z2 = 6 + 5i
z1 - z2 = -2 + 11i
z1 / z2 = 0.64 + 1.52i
z1^2 = -60 + 32i