If $$Z_1=-3-3 i$$ and $$Z_2=3-3 i$$, then the value of $$Z_1+Z_2$$ is



<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>If $$Z_1=-3-3 i$$ and $$Z_2=3-3 i$$, then the value of $$Z_1+Z_2$$ is

</textarea>If <math><semantics><mrow><msub><mi>Z</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mn>3</mn><mo>−</mo><mn>3</mn><mi>i</mi></mrow><annotation encoding="application/x-tex">Z_1=-3-3 i</annotation></semantics></math>Z​1​​=−3−3i and <math><semantics><mrow><msub><mi>Z</mi><mn>2</mn></msub><mo>=</mo><mn>3</mn><mo>−</mo><mn>3</mn><mi>i</mi></mrow><annotation encoding="application/x-tex">Z_2=3-3 i</annotation></semantics></math>Z​2​​=3−3i, then the value of <math><semantics><mrow><msub><mi>Z</mi><mn>1</mn></msub><mo>+</mo><msub><mi>Z</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">Z_1+Z_2</annotation></semantics></math>Z​1​​+Z​2​​ is
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>Given that,
$$Z_1 =-3-3 i, Z_2= 3-3 i $$
$$Z_1+Z_2 =(-3+3)+(-3 i-3 i)=0+(-6 i)=-6 i $$

</textarea>Given that, <math><semantics><mrow><msub><mi>Z</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mn>3</mn><mo>−</mo><mn>3</mn><mi>i</mi><mo separator="true">,</mo><msub><mi>Z</mi><mn>2</mn></msub><mo>=</mo><mn>3</mn><mo>−</mo><mn>3</mn><mi>i</mi></mrow><annotation encoding="application/x-tex">Z_1 =-3-3 i, Z_2= 3-3 i </annotation></semantics></math>Z​1​​=−3−3i,Z​2​​=3−3i <math><semantics><mrow><msub><mi>Z</mi><mn>1</mn></msub><mo>+</mo><msub><mi>Z</mi><mn>2</mn></msub><mo>=</mo><mo>(</mo><mo>−</mo><mn>3</mn><mo>+</mo><mn>3</mn><mo>)</mo><mo>+</mo><mo>(</mo><mo>−</mo><mn>3</mn><mi>i</mi><mo>−</mo><mn>3</mn><mi>i</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>+</mo><mo>(</mo><mo>−</mo><mn>6</mn><mi>i</mi><mo>)</mo><mo>=</mo><mo>−</mo><mn>6</mn><mi>i</mi></mrow><annotation encoding="application/x-tex">Z_1+Z_2 =(-3+3)+(-3 i-3 i)=0+(-6 i)=-6 i </annotation></semantics></math>Z​1​​+Z​2​​=(−3+3)+(−3i−3i)=0+(−6i)=−6i
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