The Complex Alternative form to the expression (5[cos(π/4) + i sin(π/4)])^3 is given as: (Option C).
What is a complex Alternate form?
A complex number of equations will take the form x + yi, where x and y are real numbers and i is an indeterminate that satisfies the rule i² = -1.
Hence, the solution to the above is given as follows:
Step 1 - Ludooph's number pi is given as:
π ≈ 3.14159265
Step 2 - Divide 3.14159265/4
= 0.78539816
Step 3
Cos (0.78539816)
= 0.70710678
It is assumed that the trigonometric angle argument is in radians.
Step 4
Divide: 3.14159265 / 4
= 0.78539816
Step 5 - find the Sin of the result of step 4
sin(0.78539816)
= 0.70710678
It is assumed that the trigonometric angle argument is in radians.
Step 6
Multiply i by the result of Step No 5
= i * 0.70710678
= 0.7071068i
Step 7 - Add the result of step no. 3 and the result of step number 6
= 0.70710678 + 0.7071068i
= 0.7071068+0.7071068i
Step 8 Multiply 5 by the result of step 7
= 5 * (0.7071068+0.7071068i)
= 5 * 0.70710678118655 + 5 * 0.70710678118655i
= 3.53553391+3.53553391i
= 3.53553391 +i(3.53553391)
= 3.5355339+3.5355339i
Step 9 - Exponentiate the results of Step 8 to the third power:
= (3.5355339+3.5355339i) ^ 3
= (5 × ei π/4)3 = 53 × ei 3 × π/4
= 125 × ei 3π/4
= -88.3883476+88.3883476i
If left in the Alternate Complex form, we have:
125[cos(3π/4) + i sin(3π/4)]
Learn more about Complex Forms at:
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