Question

Given that z₁ = 3 + 2i, z₂ = 1 - i, and z₃ = 4 + 6i, find:

(a) z₁ + z₂
(b) z₁ - 2z₂
(c) z₁z₂
(d) z₁z₃
(e) z₂z₃

Answer 1

To find the values for the expressions, substitute the given values in the expressions: (a) z₁ + z₂ = 4 + i, (b) z₁ - 2z₂ = 1 + 4i, (c) z₁z₂ = 5 - i, (d) z₁z₃ = 26i, and (e) z₂z₃ = 10 + 8i.

Step-by-step explanation:

To find the values for the expressions given, we can simply substitute the given values in the expressions.

(a) z₁ + z₂:

z₁ + z₂ = (3 + 2i) + (1 - i) = 3 + 1 + 2i - i = 4 + i

(b) z₁ - 2z₂:

z₁ - 2z₂ = (3 + 2i) - 2(1 - i) = 3 + 2i - 2 + 2i = 1 + 4i

(c) z₁z₂:

z₁z₂ = (3 + 2i)(1 - i) = 3(1) + 3(-i) + 2i(1) + 2i(-i) = 3 - 3i + 2i + 2 = 5 - i

(d) z₁z₃:

z₁z₃ = (3 + 2i)(4 + 6i) = 3(4) + 3(6i) + 2i(4) + 2i(6i) = 12 + 18i + 8i + 12i² = 12 + 26i - 12 = 26i

(e) z₂z₃:

z₂z₃ = (1 - i)(4 + 6i) = 4 - 4i + 6i - 6i² = 4 + 2i + 6i + 6 = 10 + 8i