SOLUTION: Perform the indicated operation and simplify: a) square root of -54 b) i^53 c) (3i)^7 d) (5-3i)-(2-3i) e) (3-2i)^2 f) square root of x-1 + square root of x = 1

Question 293229: Perform the indicated operation and simplify:
a) square root of -54
b) i^53
c) (3i)^7
d) (5-3i)-(2-3i)
e) (3-2i)^2
f) square root of x-1 + square root of x = 1
I would appreciate any help. Thanks in advance! :)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Perform the indicated operation and simplify:
a) square root of -54
= sqrt(-9)*sqrt(6)
= +-3i*sqrt(6)
------------------
b) i^53 = i^(52+1) = (i^4)^13*i = 1^13*i = 1*i = i
------------------
c) (3i)^7 = 2187*i^4*i^3 = 2187*1*(-i) = -2187i
------------------
d) (5-3i)-(2-3i) = (5-2)+(-3--3)i = 3+0i = 3
------------------
e) (3-2i)^2 = 9 -2(3)(2i) + (2i)^2 = (9-4)-12i = 5-12i
------------------
f) square root of x-1 + square root of x = 1
sqrt(x-1) + sqrt(x) = 1
sqrt(x-1) = 1-sqrt(x)
x-1 = 1-2sqrt(x)+x
-2 = -2sqrt(x)
sqrt(x) = 1
x = 1
=============
Cheers,
Stan H.
=============

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