Posted by **jack** on Sunday, October 16, 2011 at 10:54am.

I Wanted To Find The Square Root Of (1-2i)

But I Didn't Know How To Solve It.

My Solution :

x+yi = sqr(1-2i)

x2-y2+2xyi = 1- 2i

x2-y2 = 1

2xy = -2

y = - 1/x

x2 - (-1/x) = 1 ] * x2

x4-x2-1 = 0

How To Evaluated (x4-x2-1) ?

I Tried To Sol

- math -
**bobpursley**, Sunday, October 16, 2011 at 12:18pm
I would convert the complex number to polar.

1-2i= sqrt5 @arctan-2=sqrt 5 @-63.4349488 degrees or @(360-63.43)deg figure that angle out.

sqrt (1-2i)= sqrt(sqrt5)@1/2 (that angle)

now convert back to polar.

lets do it so it can be checked.

(5^.25)=1.49534878

that angle= = 296.565051

1/2 that angle= = 148.282525

sqrt(1-2i)=1.4953cos 148.282525+i(1.4953sin 148.282525)

= -1.27-i*0.786

Now, just for fun sake,lets square that.

(-1.27^2)-(..786^2)-2i(1.21*.786)

= 1.61-.617 -i 1.90=.99-1.9i

Ok, you can work it with more accuracy to get it.

## Answer This Question

## Related Questions

- algebra - 1.)correct 2.)wrong---> the first term is wrong 4(3a^2)^2 = 36a^4 3...
- ALGEBRA - 1, Factor each expression x^2 - 10x - 24 A. (x + 4)(x - 6) B. (x + 6)(...
- Algebra2/Trig - sqr(x^2-4)+(x^2)/x^2+1 I got ((x^2+1)*sqr(x^2-4)+x^2)/x^2+1 But ...
- Math - Find the quotient function f/g for f(x)=sqr(x+1) and g(x)= sqr( x-1). My...
- Math - Find the quotient function f/g for f(x)=sqr(x+1) and g(x)= sqr( x-1). My ...
- Algebra - Use the quadratic formula to solve the equation. Give exact answers: ...
- Math Help! - Four students worked to find an estimate for square root 22. Who is...
- algebra - 1)Write the expression 9n^6+7n^3-6 in quadratic form,if possible A.9(n...
- Math simplifying mixed radicals - Please help me simplify these following mixed ...
- Math - What are the solution sets of the following 3 problems,the square root of...

More Related Questions