simplify (6+3i)(6-3i)

{ "query": { "display": "simplify $$\\left(6+3i\\right)\\left(6-3i\\right)$$", "symbolab_question": "SIMPLIFY#simplify (6+3i)(6-3i)" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "45", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\left(6+3i\\right)\\left(6-3i\\right)=45$$", "input": "\\left(6+3i\\right)\\left(6-3i\\right)", "steps": [ { "type": "step", "primary": "Apply complex arithmetic rule: $$\\left(a+bi\\right)\\left(a-bi\\right)=a^{2}+b^{2}$$", "result": "=6^{2}+3^{2}" }, { "type": "interim", "title": "$$6^{2}+3^{2}=45$$", "input": "6^{2}+3^{2}", "steps": [ { "type": "interim", "title": "$$6^{2}=36$$", "input": "6^{2}", "steps": [ { "type": "step", "primary": "$$6^{2}=36$$", "result": "=36" } ], "meta": { "interimType": "N/A" } }, { "type": "interim", "title": "$$3^{2}=9$$", "input": "3^{2}", "steps": [ { "type": "step", "primary": "$$3^{2}=9$$", "result": "=9" } ], "meta": { "interimType": "N/A" } }, { "type": "step", "result": "=36+9" }, { "type": "step", "primary": "Add the numbers: $$36+9=45$$", "result": "=45" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7CCwlHprwwOhseNCskjSi296GQqufR6tr2vPxOUv7H+/NI0xTNv3Zl/W2YhU4zsN+pHme/oXFA7pRQSy1hI3AUTjLHiWnSMZXp27Y119ujqc=" } }, { "type": "step", "result": "=45" } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }