Find the midpoint $$m$$ of $$Z_1=7+8 i$$ and $$Z_2=8-7 i$$ ( Express your answer in rectangular form)



<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>Find the midpoint $$m$$ of $$Z_1=7+8 i$$ and $$Z_2=8-7 i$$ ( Express your answer in rectangular form)

</textarea>Find the midpoint <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><mn>7</mn><mo>+</mo><mn>8</mn><mi>i</mi></mrow><annotation encoding="application/x-tex">Z_1=7+8 i</annotation></semantics></math>Z​1​​=7+8i and <math><semantics><mrow><msub><mi>Z</mi><mn>2</mn></msub><mo>=</mo><mn>8</mn><mo>−</mo><mn>7</mn><mi>i</mi></mrow><annotation encoding="application/x-tex">Z_2=8-7 i</annotation></semantics></math>Z​2​​=8−7i ( Express your answer in rectangular form)
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>If the points are $$Z_1=7+8i$$ and $$Z_2=8-7i$$ 
Then midpoint m=$$\frac{Z_1+Z_2}{2}$$ 
$$=\frac{(1+8)+(8i-7i)}{2}$$ 
$$=\frac{15+i}{2}$$ 
</textarea>If the points are <math><semantics><mrow><msub><mi>Z</mi><mn>1</mn></msub><mo>=</mo><mn>7</mn><mo>+</mo><mn>8</mn><mi>i</mi></mrow><annotation encoding="application/x-tex">Z_1=7+8i</annotation></semantics></math>Z​1​​=7+8i and <math><semantics><mrow><msub><mi>Z</mi><mn>2</mn></msub><mo>=</mo><mn>8</mn><mo>−</mo><mn>7</mn><mi>i</mi></mrow><annotation encoding="application/x-tex">Z_2=8-7i</annotation></semantics></math>Z​2​​=8−7i Then midpoint m=<math><semantics><mrow><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></mrow><annotation encoding="application/x-tex">\frac{Z_1+Z_2}{2}</annotation></semantics></math>​2​​Z​1​​+Z​2​​​​ <math><semantics><mrow><mo>=</mo><mfrac><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mn>8</mn><mo>)</mo><mo>+</mo><mo>(</mo><mn>8</mn><mi>i</mi><mo>−</mo><mn>7</mn><mi>i</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><annotation encoding="application/x-tex">=\frac{(1+8)+(8i-7i)}{2}</annotation></semantics></math>=​2​​(1+8)+(8i−7i)​​ <math><semantics><mrow><mo>=</mo><mfrac><mrow><mn>1</mn><mn>5</mn><mo>+</mo><mi>i</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><annotation encoding="application/x-tex">=\frac{15+i}{2}</annotation></semantics></math>=​2​​15+i​​ 
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