Question

Complex number question

Answer 1

The complex number \[zi = \frac{ a }{ 1+i } \] and \[z2=\frac{ b }{ 1+2i}\] where a and b are real are such that
zi+z2= 1 . Find a and b

Answer 2

it is like you would with surds, you want a real number on the bottom so for example

\[z _{1}= \frac{ a (1-i)}{ (1+i)(1-i) }\]
\[z_{2}= \frac{b(1-2i)}{ (1+2i)(1-2i) }\]

Answer 3

then you know how to add fractions of real numbers, then you just add the fractions and solve for a and b since you know it will equal 1
you will compare the real and imaginary parts

Answer 4

Thanks dozennss !!

Answer 5

need me to check your answer or are you okay?

Answer 6

Its totally fine :) have the final answers and got them right :)