Simplify ( square root of 2-i)^4

Problem

(√(,2−i))4

Solution

1. Rewrite the expression using exponent rules. Since the square root is equivalent to the power of 1/2 the expression becomes ((2−i)(1/2))4

2. Multiply the exponents. Using the rule (am)n=a(m⋅n) we calculate 1/2⋅4=2

3. Simplify the expression to a squared binomial. The expression is now (2−i)2

4. Expand the binomial using the formula (a−b)2=a2−2*a*b+b2

(2−i)2=2−2*(2)*(i)+i2

5. Substitute the value of i2 Since i is the imaginary unit, i2=−1

4−4*i+(−1)

6. Combine the real parts. Subtract 1 from 4 to get the final simplified form.

3−4*i

Final Answer

(√(,2−i))4=3−4*i

Want more problems? Check here!