Find the average $$m$$ of $$Z_1=-8-4 i$$ and $$Z_2=-12+i$$



<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>Find the average $$m$$ of $$Z_1=-8-4 i$$ and $$Z_2=-12+i$$

</textarea>Find the average <math><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math>m of <math><semantics><mrow><msub><mi>Z</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mn>8</mn><mo>−</mo><mn>4</mn><mi>i</mi></mrow><annotation encoding="application/x-tex">Z_1=-8-4 i</annotation></semantics></math>Z​1​​=−8−4i and <math><semantics><mrow><msub><mi>Z</mi><mn>2</mn></msub><mo>=</mo><mo>−</mo><mn>1</mn><mn>2</mn><mo>+</mo><mi>i</mi></mrow><annotation encoding="application/x-tex">Z_2=-12+i</annotation></semantics></math>Z​2​​=−12+i
</div>

<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>If the point are $$Z_1=-8-4 i, Z_2=-12+i$$
then average $$m=\frac{Z_1+Z_2}{2}=\frac{(-8-4 i)+(-12+i)}{2}$$
$$=\frac{(-8-12)+i(-4+1)}{2} $$
$$=\frac{-20+i(-3)}{2}=-10-\frac{3}{2}i $$
</textarea>If the point are <math><semantics><mrow><msub><mi>Z</mi><mn>1</mn></msub><mo>=</mo><mo>−</mo><mn>8</mn><mo>−</mo><mn>4</mn><mi>i</mi><mo separator="true">,</mo><msub><mi>Z</mi><mn>2</mn></msub><mo>=</mo><mo>−</mo><mn>1</mn><mn>2</mn><mo>+</mo><mi>i</mi></mrow><annotation encoding="application/x-tex">Z_1=-8-4 i, Z_2=-12+i</annotation></semantics></math>Z​1​​=−8−4i,Z​2​​=−12+i then average <math><semantics><mrow><mi>m</mi><mo>=</mo><mfrac><mrow><msub><mi>Z</mi><mn>1</mn></msub><mo>+</mo><msub><mi>Z</mi><mn>2</mn></msub></mrow><mrow><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>(</mo><mo>−</mo><mn>8</mn><mo>−</mo><mn>4</mn><mi>i</mi><mo>)</mo><mo>+</mo><mo>(</mo><mo>−</mo><mn>1</mn><mn>2</mn><mo>+</mo><mi>i</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><annotation encoding="application/x-tex">m=\frac{Z_1+Z_2}{2}=\frac{(-8-4 i)+(-12+i)}{2}</annotation></semantics></math>m=​2​​Z​1​​+Z​2​​​​=​2​​(−8−4i)+(−12+i)​​ <math><semantics><mrow><mo>=</mo><mfrac><mrow><mo>(</mo><mo>−</mo><mn>8</mn><mo>−</mo><mn>1</mn><mn>2</mn><mo>)</mo><mo>+</mo><mi>i</mi><mo>(</mo><mo>−</mo><mn>4</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><annotation encoding="application/x-tex">=\frac{(-8-12)+i(-4+1)}{2} </annotation></semantics></math>=​2​​(−8−12)+i(−4+1)​​ <math><semantics><mrow><mo>=</mo><mfrac><mrow><mo>−</mo><mn>2</mn><mn>0</mn><mo>+</mo><mi>i</mi><mo>(</mo><mo>−</mo><mn>3</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></mfrac><mo>=</mo><mo>−</mo><mn>1</mn><mn>0</mn><mo>−</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi>i</mi></mrow><annotation encoding="application/x-tex">=\frac{-20+i(-3)}{2}=-10-\frac{3}{2}i </annotation></semantics></math>=​2​​−20+i(−3)​​=−10−​2​​3​​i
</div>