How do you simplify sqrt(-4) - sqrt(-25)425?

2 Answers
Aug 3, 2018

z=-3i orz=3iz=3iorz=3i

Explanation:

We know for the complex numbers : i^2=-1i2=1

Let ,

z=sqrt(-4)-sqrt(-25)z=425

=>z=sqrt(4(-1))-sqrt(25(-1))z=4(1)25(1)

=>z=sqrt(4i^2)-sqrt(25i^2)z=4i225i2

=>z=sqrt((2i)^2)-sqrt((5i^2))z=(2i)2(5i2)

=>z=(+-2i)-(+-5i)z=(±2i)(±5i)

=>z=(2i)-(5i) or z=(-2i)-(-5i)z=(2i)(5i)orz=(2i)(5i)

=>z=-3i orz=3iz=3iorz=3i

Aug 3, 2018

pm3i±3i

Explanation:

Recall that sqrt(-1)=i1=i. With this in mind, we can rewrite this as

sqrt4sqrt(-1)-(sqrt(25)sqrt(-1))41(251)

=>+-2i-(+-5i)±2i(±5i)

=>2i-5i=-3i2i5i=3i and -2i-(-5i)=5i-2-=3i2i(5i)=5i23i

Therefore, our solutions are pm3i±3i.

Hope this helps!