+0  
 
-1
156
3
avatar+41 

Find all complex numbers  such that .

Write your solutions in  form, separated by commas. So, "1+2i, 3-i" is an acceptable answer format, but "2i+1; -i+3" is not. (Don't include quotes in your answer.)

Note: This problem is not about functions.

 Jul 16, 2021
 #1
avatar+2266 
0

The question isn't showing for me.

 

=^._.^=

 Jul 16, 2021
 #2
avatar+41 
+1

Sorry!

Find all complex numbers $z$ such that $z^2 = 2i$.  Write your solutions in $a+bi$ form, separated by commas. So, "1+2i, 3-i" is an acceptable answer format, but "2i+1; -i+3" is not. (Don't include quotes in your answer.)  Note: This problem is not about functions.

 Jul 16, 2021
 #3
avatar+2266 
+2

(a+bi)^2 = 2i

a^2 - b^2 + 2abi = 2i

a^2 - b^2 = 0

a^2 = b^2

2abi = 2i

ab = 1

 

a^2 = b^2 and ab = 1

From ab = 1, we know that either a and b are both positive or both negative, that means we can say that a = b from a^2 = b^2. 

a = b and ab = 1

a = 1, b = 1, or a = -1, b = - 1

(1 + i) or (-1 - i)

 

=^._.^=

catmg  Jul 16, 2021

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