z1=[cos pi/4 +sin pi/4] z2= [cos 2pi+sin 2pi]

z1= sqrt 5 solve.

how do you do this? substitute z1 and do what?

actually, z1 = cos pi/4 +sin pi/4 i

that is (1,π/4)
z2 = (1,2π) = (1,0)

no idea how you can say z1=√5, when you already said is is (1,π/4)

z1*z2 = (1,π/4)
z1+z2 = (1/√2 + 1/√2 i)+(1+0i) = (1+1/√2)+1/√2 i

|z1+z2| = √((1+1/√2)^2 + 1/2) = √(2+√2)

I can't fathom just what the question is, much less the answer...

To solve for z1, we will substitute the given value of z1, which is z1 = cos(pi/4) + sin(pi/4), into the equation and then simplify it.

Let's break it down step by step:

1. Start with the given equation: z1 = cos(pi/4) + sin(pi/4).

2. Recall the trigonometric identity: cos(pi/4) = sin(pi/4) = sqrt(2)/2.

3. Substitute the values into the equation: z1 = sqrt(2)/2 + sqrt(2)/2.

4. Combine the terms on the right side of the equation: z1 = (sqrt(2) + sqrt(2))/2.

5. Simplify the expression: z1 = (2 * sqrt(2))/2.

6. Simplify further: z1 = sqrt(2).

Therefore, the solution for z1 is z1 = sqrt(2).