Question Type 2: Working with conjugate of complex numbers Exercises

Find the conjugate of $-2 + 5i$ and then compute the product of the number with its conjugate.

Find the conjugate of the complex number $4 - 3i$.

Multiply the complex number $4 - 3i$ by its conjugate and simplify the result.

Solve for $z$ if ar z=2+3i.

Compute the modulus of $5 - 12i$ by using its conjugate.

Let $z=x+yi$. Show that zar z=x^2+y^2.

Simplify rac{5 + 3i}{2 + 3i} and write your answer in the form $a + bi$.

Simplify the expression rac{3 + 2i}{1 - i} by rationalizing the denominator.

Express rac{1}{1 + i} in the form $a + bi$.

Simplify rac{2 - 3i}{4 + i} and express your answer in the form $a + bi$.

Let $z=x+yi$ satisfy z+ar z=10. Find the value of $y$.

Simplify the expression rac{1+2i}{3-4i} + rac{5 - i}{2 + i} and express the result in the form $a + bi$.