Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
5123−512i
Evaluate
(−23−2i)5
Write 5 as sum
(−23−2i)2+3
Use am+n=am×an to expand the expression
(−23−2i)2(−23−2i)3
Multiply
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Evaluate
(−23−2i)2
Use (a−b)2=a2−2ab+b2 to expand the expression
(−23)2−2(−23)×2i+(2i)2
Multiply
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Multiply the terms
2(−23)×2i
Rewrite the expression
−2×23×2i
Multiply the terms
−43×2i
Multiply the numbers
−83×i
(−23)2+83×i+(2i)2
Evaluate the power
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Evaluate
(2i)2
Evaluate
22i2
Evaluate the power
4i2
Evaluate the power
−4
(−23)2+83×i−4
Calculate
12+83×i−4
Simplify the expression
8+83×i
(8+83×i)(−23−2i)3
Multiply
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Evaluate
(−23−2i)3
Use (a−b)3=a3−3a2b+3ab2−b3 to expand the expression
(−23)3−3(−23)2×2i+3(−23)(2i)2−(2i)3
Evaluate
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Evaluate
(−23)3
Evaluate the power
−8×33
Multiply the terms
−243
−243−3(−23)2×2i+3(−23)(2i)2−(2i)3
Evaluate
−243−72i+3(−23)(2i)2−(2i)3
Evaluate
More Steps
Evaluate
3(−23)(2i)2
Evaluate the power
3(−23)(−4)
Rewrite the expression
3×23×4
Multiply the terms
243
−243−72i+243−(2i)3
Evaluate
More Steps
Evaluate
−(2i)3
Evaluate the power
−(−8i)
Calculate
8i
−243−72i+243+8i
Simplify the expression
−64i
(8+83×i)(−64i)
Apply the distributive property
8(−64i)+83×i(−64i)
Multiply the numbers
−512i+83×i(−64i)
Multiply the numbers
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Evaluate
83×i(−64i)
Multiply
83×(−64)i2
Multiply
−5123×i2
Use i2=−1 to transform the expression
−5123×(−1)
Calculate
5123
−512i+5123
Solution
5123−512i
Show Solution
