Question

Please answer this question !

Answer 1

Step-by-step explanation:

We have,

$z = ( \sqrt{2} - \sqrt{ - 4} )^{2} - 3(2 + 4i)(3 - 2i) + (1 - i)^{3}$

$\implies \: z = ( \sqrt{2} - 2i )^{2} - 3 \{6 + 12 i - 4i - 8 {i}^{2} \} + \{{(1)}^{3} - 3.( {1})^{2} .i + 3.(1). {(i)}^{2} - {(i)}^{3} \}$

$\implies \: z = \{( \sqrt{2})^{2} + (2i )^{2} - 2. \sqrt{2} .2i \} - 3 \{6 + 12 i - 4i - 8 {i}^{2} \} + \{{(1)}^{3} - 3.( {1})^{2} .i + 3.(1). {(i)}^{2} - {(i)}^{3} \}$

$\implies \: z = \{2 - 4 - 4\sqrt{2} i \} - 3 \{6 + 8 i + 8 \} + \{1 - 3i - 3 - i \}$

$\implies \: z = - 2 - 4\sqrt{2} i -42 - 24 i - 2- 4i$

$\implies \: z = - 46- (28 + 4\sqrt{2}) i$

So,

$\: Im(z) = - 28 - 4 \sqrt{2}$