Question
Simplify the expression
1+22×i
Evaluate
1−2×i5+2×i
Multiply by the Conjugate
(1−2×i)(1+2×i)(5+2×i)(1+2×i)
Calculate
More Steps

Evaluate
(5+2×i)(1+2×i)
Apply the distributive property
5+52×i+2×i+2×i2×i
Multiply the numbers
More Steps

Evaluate
2×i2×i
Multiply
2×2×i2
Multiply
2i2
Use i2=−1 to transform the expression
2(−1)
Calculate
−2
5+52×i+2×i−2
Calculate
3+52×i+2×i
Calculate
More Steps

Evaluate
52×i+2×i
Collect like terms by calculating the sum or difference of their coefficients
(5+1)2×i
Calculate
62×i
3+62×i
(1−2×i)(1+2×i)3+62×i
Calculate
More Steps

Evaluate
(1−2×i)(1+2×i)
Use (a−b)(a+b)=a2−b2 to simplify the product
12−(2×i)2
Evaluate the power
1−(2×i)2
Evaluate the power
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Evaluate
(2×i)2
Evaluate
(2)2i2
Reduce the index of the radical and exponent with 2
2i2
Evaluate the power
−2
1−(−2)
Calculate
3
33+62×i
Rewrite the expression
33(1+22×i)
Solution
1+22×i
Show Solution
