$${1 + 5} {i}$$ Lies in which quadrant the complex plane?



<div id="displayOption0" class="markdown-body editormd-html-preview"><textarea>$$1^{st}$$ quadrant</textarea><math><semantics><mrow><msup><mn>1</mn><mrow><mi>s</mi><mi>t</mi></mrow></msup></mrow><annotation encoding="application/x-tex">1^{st}</annotation></semantics></math>1​st​​ quadrant
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<div id="displayOption1" class="markdown-body editormd-html-preview"><textarea>$$2^{nd}$$ quadrant</textarea><math><semantics><mrow><msup><mn>2</mn><mrow><mi>n</mi><mi>d</mi></mrow></msup></mrow><annotation encoding="application/x-tex">2^{nd}</annotation></semantics></math>2​nd​​ quadrant
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<div id="displayOption2" class="markdown-body editormd-html-preview"><textarea>$$3^{rd}$$ quadrant</textarea><math><semantics><mrow><msup><mn>3</mn><mrow><mi>r</mi><mi>d</mi></mrow></msup></mrow><annotation encoding="application/x-tex">3^{rd}</annotation></semantics></math>3​rd​​ quadrant
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<div id="displayOption3" class="markdown-body editormd-html-preview"><textarea>$$4^{th}$$ quadrant</textarea><math><semantics><mrow><msup><mn>4</mn><mrow><mi>t</mi><mi>h</mi></mrow></msup></mrow><annotation encoding="application/x-tex">4^{th}</annotation></semantics></math>4​th​​ quadrant
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<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>$${1 + 5} {i}$$ Lies in which quadrant the complex plane?

</textarea><math><semantics><mrow><mrow><mn>1</mn><mo>+</mo><mn>5</mn></mrow><mrow><mi>i</mi></mrow></mrow><annotation encoding="application/x-tex">{1 + 5} {i}</annotation></semantics></math>1+5i Lies in which quadrant the complex plane?
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>Comparing with, $$x+iy$$, here $$x=1,y=5$$
Since, $$x$$ and $$y$$ both are +ve. Hence, $$1+5i$$ lies in $$1^{st}$$ quadrant.
</textarea>Comparing with, <math><semantics><mrow><mi>x</mi><mo>+</mo><mi>i</mi><mi>y</mi></mrow><annotation encoding="application/x-tex">x+iy</annotation></semantics></math>x+iy, here <math><semantics><mrow><mi>x</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mi>y</mi><mo>=</mo><mn>5</mn></mrow><annotation encoding="application/x-tex">x=1,y=5</annotation></semantics></math>x=1,y=5 Since, <math><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math>x and <math><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math>y both are +ve. Hence, <math><semantics><mrow><mn>1</mn><mo>+</mo><mn>5</mn><mi>i</mi></mrow><annotation encoding="application/x-tex">1+5i</annotation></semantics></math>1+5i lies in <math><semantics><mrow><msup><mn>1</mn><mrow><mi>s</mi><mi>t</mi></mrow></msup></mrow><annotation encoding="application/x-tex">1^{st}</annotation></semantics></math>1​st​​ quadrant.
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