math 110 college algebra

Question

Express 2-3i/3+1 in the form a + bi.

Answer 1

If your question is

(2-3i) ⁄ (3+i) the solution is,

(2 - 3i) / (3+i) = ((2 - 3i) × (3 - i)) ⁄ ((3+i) ×(3 -i)) (multiplying numerator and denominator with conjugate of 3+i which is 3 - i ), then,

(2 - 3i) / (3+i) = (6 - 6i -9i - 3) ⁄ 10 ( simple cross multiplication) Simplifying,

(2 - 3i) / (3+i) = (3 - 15i) ⁄ (10)

(2 - 3i) / (3+i) = (3 ⁄ 10) + (3 ⁄ 2)i (where in the form a+bi in which a = 3 ⁄ 10 and b = 3 ⁄ 2)