Question

已知复数（1+i）的3次方×（a-i）的平方÷根号2×（a+3i）的平方 的模是3分之2,求a.时间急啊………求大哥大姐

Answer 1

| [(1 + i)^3 · (a - i)^2] / [√2 (a + 3i)^2] | = 2/3

2 | (a - i)^2 / (a + 3i)^2 | = 2/3

| (a - i)^2 / (a + 3i)^2 | = 1/3

| (a^2 - 1 - 2ai)/(a^2 + 6ai - 9) | = 1/3

当 (a^2 - 1 - 2ai)/(a^2 + 6ai - 9) < 0

- (a^2 - 1 - 2ai)/(a^2 + 6ai - 9) = 1/3

(a^2 - 3)/(a + 3i) = 0

a^2 = 3

==> a = √3 或 a = - √3

当 (a^2 - 1 - 2ai)/(a^2 + 6ai - 9) > 0

(a^2 - 1 - 2ai)/(a^2 + 6ai - 9) = 1/3

(a - 3i)^2 = - 12

==> a = (3 - 2√3)i 或 a = (3 + 2√3)i